---
slug: rock-paper-lizard
passed: 2026-10-14
by: the assay line (research/assay-line/cited-1014/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex
checked: 201
confirmed: 179
wrong: 21
unverifiable: 0
observed: 0
stale: 1
---

This was the directed cited-1014 correction pass for rock-paper-lizard at 4bec84fb04. The fixer re-read the evidence for every edited triage item, corrected the authored HTML, markdown and verifier, and recorded all 22 dispositions. The 179 CONFIRMED entries below carry the earlier Codex checker's source rereads from N2-codex.md at 67088387e0, with that provenance and its limited interpretations retained; they are not presented as 179 new independent rereads by the fixer. Confirmed wording superseded by this triage is updated to the corrected claim. The wrong count includes 11 WRONG and 10 MINOR lines; nine MINOR items remain unchanged by explicit triage decision.

## Claims

- WRONG | X1: "Nobody expected to find it written into an animal." | https://news.ucsc.edu/2007/10/three-way-mating-game-of-north-american-lizard-found-in-distant-european-relative/ | Re-read the UCSC article, paragraph on predictions: Wright (1968) and Maynard Smith (1982) preceded the 1996 lizard report. The universal surprise claim fails.
- MINOR | X2: "three strategies hard-wired and heritable." | https://frankino.uh.edu/assets/docs/sinervoetal.pdf | N2 reports yellow-to-partial-blue phenotypic change in the primary study. Heritability remains supported; hard-wired is a loose lifetime-immutability implication. Listed per triage, not independently re-read here.
- MINOR | X3: "a sneaker can't fool a male who never looks away." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | N2 reports infrequent blue/yellow shared paternity. This qualifies the guarding metaphor without reversing the blue advantage. Listed per triage, not independently re-read here.
- WRONG | X4: "the only resting state is the dead centre" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | Re-read Hofbauer and Sigmund pp. 482 and 484. All corners are rest points; the page RHS gives zero there and at the centre. Only the centre is interior; corners are unstable.
- MINOR | X5: "Every starting mix circles it forever on a closed orbit." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Hofbauer and Sigmund restrict circulation to noncentral interior starts. The actual RHS vanishes at the centre and corners, and is [0.25,-0.25,0] at [0.5,0.5,0]. Listed as MINOR per triage.
- MINOR | X6: "Drag a starting point into the triangle and let it run." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:425-433 | The authored page registers a click listener and no drag handler for this instrument. The caption correctly says to click. Listed as the triage gesture-instruction near-miss.
- WRONG | X7: "tilt < 0 spirals outward until two morphs die." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | Re-read pp. 482 and 484: initially positive frequencies remain positive, and outward trajectories approach the full boundary cycle. The code has no demographic extinction rule.
- WRONG | X8: "until a morph hits zero and the cycle breaks" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | The same invariant-interior result excludes finite-time loss and a permanent two-player survivor state in this ODE. Finite random populations are a different model.
- WRONG | X9: "It is the only arrangement in which three strategies can all keep existing" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf; https://www.ma.imperial.ac.uk/~dturaev/project1-literature.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | Re-read p. 486: an interior ESS is globally stable. For A=-I and u=(1/3,1/3,1/3), u^T A x-x^T A x=sum(x_i^2)-1/3>0 away from u. The page integrator comes within 1e-12 of u from [0.6,0.3,0.1] at t=100 without cyclic dominance.
- WRONG | X10: "all three persist indefinitely" | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Re-read Kerr pp. 173-174: the robustness results report at least 66 generations, and Methods terminate the experiments after one week, approximately 66 generations. This does not establish indefinite persistence.
- WRONG | X11: "a cell can be invaded by a neighbour that beats it." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:460-482,499; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | Re-read Kerr p. 171 and evaluated the authored lattice predicate with its labels. It ran C>R>S>C; Kerr gives C>S>R>C. The prose and Instrument 1 already had the correct directions.
- WRONG | X12: "all three coexist forever" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:454-483; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | The 120 by 120 random grid has absorbing single-type states. Before the fix, the legal local invasion sequence (target,neighbour)=(1,0),(0,120),(1,121) from [14398,1,1] counts reaches [14400,0,0]. The corresponding relabelled path remains legal after the biological mapping repair.
- MINOR | X13: "Arrow proved no fair rule can untangle the knot." | https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/arrow.pdf | N2 identifies Arrow formal assumptions; fair is an informal compression, not an unrestricted theorem about every possible rule. Listed per triage, not independently re-read here.
- WRONG | X14: "The dominance directions above are exactly as the two Nature papers record them;" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:460-482,499; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | The assurance was false for Instrument 3 because all three bacterial edges were reversed. Correcting that mapping makes it agree with Kerr p. 171; no change to the correct lizard cycle is needed.
- MINOR | X15: "Everything numeric is recomputed in front of you and re-derived offline" | git show 67088387e0:research/rock-paper-lizard/verify.mjs:284-301; git show 67088387e0:public/strata/rock-paper-lizard/index.html:144,232 | Read the complete verifier: selected mathematical checks and broad DOI/name/zero-token checks do not cover every number or the lattice. This is MINOR by the directing rule. The N2 mutation result is prior evidence, not rerun here.
- MINOR | X16: "three competing species" | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Kerr pp. 171-172 identify strains of E. coli; the page labels three bacterial strains. The accessible-description terminology remains the listed MINOR item.
- WRONG | X17: "orbits spiral out until a morph hits zero and the cycle breaks." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf; research/assay-line/cited-1014/rock-paper-lizard/verify-fixes.mjs | Read the runtime branch and RHS/step. The negative-tilt readout incorrectly turns asymptotic boundary approach into finite-time death; no extinction event is implemented.
- MINOR | X18: "a well-mixed flask collapses to a single strain (Reichenbach, Mobilia & Frey, Nature 2007)." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://www.nature.com/articles/nature06095 | Re-read Kerr pp. 172-174 and Reichenbach author manuscript pp. 2-6: Kerr supplies the flask experiment; Reichenbach supplies the mobility-threshold model. Citation placement is repaired in the dek sentence already edited for X7/X8/X17.
- WRONG | X19: "eight triples in a ring with no best pick." | https://arxiv.org/pdf/1406.2212 | Re-read Brofos pp. 3-4 and solved exact prefix-state races. HHT>HTT>TTH>THH>HHT has probabilities 2/3,3/4,2/3,3/4. HHH and TTT never exceed 1/2 against another triple, so neither belongs to a strict dominance ring. Every first choice has a better response.
- MINOR | X20: "Arrow's proof that no fair rule can untangle it." | https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/arrow.pdf | This is the metadata copy of X13. Arrow specified ranking conditions are compressed into informal fairness language. Listed per triage, not independently re-read here.
- MINOR | X21: "Every number recomputed in the browser and checked offline." | git show 67088387e0:research/rock-paper-lizard/verify.mjs:284-301; git show 67088387e0:public/strata/rock-paper-lizard/index.html:144,232 | This is the JSON-LD copy of X15. Reading the verifier confirms that presence checks and selected calculations do not validate every numerical sentence. The date change affects a different JSON property.
- STALE | X22: ""dateModified":"2026-06-18"" | git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md; git log 67088387e0 -- public/strata/rock-paper-lizard/index.html | The initial page date was 2026-06-18, but read-only git history includes the 2026-10-01 change 2e60bcb5dd1. The current correction sets dateModified to 2026-10-14 under the explicit JSON-LD exception.

- CONFIRMED | "system orange ▸ blue ▸ yellow ▸ orange" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [header-cycle]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "rank-able 0%" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [header-ranking]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "period ~6 yr" | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [header-period]; The six-year period is the result attributed to the 1996 study, not a claim about every later population or observation.
- CONFIRMED | "A children's game is a fair tie: rock, paper, scissors, each beating exactly one of the others, none of them best." | https://www.nature.com/articles/nature00823 | Prior Codex N2 source check [game-rules]; The three game choices each beat one other choice and lose to one.
- CONFIRMED | "But a lizard in the California scrub plays it for real" [...] "three kinds of male, none able to win, all kept alive by the very fact that the ring never closes on a champion." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [lizard-coexistence-intro]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "Every spring on the rocky slopes of the inner Coast Range, male Uta stansburiana" [...] "the common side-blotched lizard" [...] "sort themselves by the colour of their throats." | https://science.ucsc.edu/pandemic-stories-why-i-am-alone-in-the-desert-catching-lizards/ | Prior Codex N2 source check [spring-location]; The field account describes spring work in the inner Coast Range of California; the primary study also locates the rocky outcrops and spring maturation.
- CONFIRMED | "The orange males are bullies: big, aggressive, holding large territories with many females." | https://frankino.uh.edu/assets/docs/sinervoetal.pdf | Prior Codex N2 source check [orange-strategy]; The primary study reports greater orange-male mass at maturity, aggression, and large territories.
- CONFIRMED | "The blue males are guardians: smaller territories, usually one female, watched closely." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf; https://citeseerx.ist.psu.edu/document?doi=64e78f4d456b7de1f323ab453c73d2aa12c67330&repid=rep1&type=pdf | Prior Codex N2 source check [blue-strategy]; The primary paper supports smaller blue territories and close guarding. The single-female description additionally comes from Durrett, Stochastic Spatial Models, p. 491, which N2 read as indexed PDF text; the direct open failed.
- CONFIRMED | "The yellow males own nothing" [...] "their throats mimic the colouring of a receptive female, and they use the disguise to sneak matings on territory they could never hold." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [yellow-strategy]; The source describes the nonterritorial female-mimicking yellow tactic. This does not rule out later phenotypic change.
- CONFIRMED | "When orange bullies dominate, their territories are so large and so full of females that they cannot guard them all" [...] "and yellow sneakers, slipping past in female costume, clean up. So yellow rises." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [yellow-invasion]; The paper describes orange intrusion, yellow exploitation of orange territories, and blue reduction of yellow cuckoldry.
- CONFIRMED | "And a population of blue guards, each holding a small patch, is easy meat for an orange bully who simply takes the patch by force. So orange rises" [...] "and we are back where we started." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [orange-invasion]; The paper describes orange intrusion, yellow exploitation of orange territories, and blue reduction of yellow cuckoldry.
- CONFIRMED | "Orange beats blue beats yellow beats orange." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [pull-dominance]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "No throat colour is best." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [pull-no-best]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "Whichever is winning is sowing the conditions for the one that beats it." | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [pull-frequency]; The paper supports cyclic frequency-dependent advantage. It does not establish a rare-type advantage against every possible population composition.
- CONFIRMED | "Barry Sinervo and Curtis Lively reported this in Nature in 1996, and gave it the only name that fits: the rock–paper–scissors game." | https://www.nature.com/articles/380240a0; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [sinervo-report]; The publisher record and later study support the named authors, strategies, cycle, and attributed 1996 six-year result.
- CONFIRMED | "The morph frequencies oscillate, they found, over roughly a six-year cycle" [...] "orange peaks, then yellow, then blue, then orange" [...] "driven by negative frequency-dependent selection: each strategy does best precisely when it is rare, and worst when it is common." | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [six-year-oscillation]; The six-year period is the result attributed to the 1996 study, not a claim about every later population or observation.
- CONFIRMED | "orange peaks, then yellow, then blue, then orange" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://science.ucsc.edu/pandemic-stories-why-i-am-alone-in-the-desert-catching-lizards/ | Prior Codex N2 source check [peak-order]; The documented dominance cycle and the later field account support the stated order of morph peaks.
- CONFIRMED | "each strategy does best precisely when it is rare, and worst when it is common." | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [negative-frequency-definition]; The paper supports cyclic frequency-dependent advantage. It does not establish a rare-type advantage against every possible population composition.
- CONFIRMED | "The game has no equilibrium any one type can rest at. It has a cycle." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [no-type-equilibrium]; The interior point is the RPS Nash equilibrium. This wording is supported as the absence of a stable pure-game solution; corners remain dynamical rest points, as X4 now explains.
- CONFIRMED | ""Beats" here is not a ladder; it is a loop. And a loop is the one shape a ranking provably cannot hold." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [loop-not-ladder]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "You can measure exactly how much of a contest a ranking can hold." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [ranking-measurable]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "Treat the head-to-head results as a flow on a triangle" [...] "an arrow on each edge pointing from loser to winner" [...] "and split that flow into two parts, the way you'd split a wind field into the part that flows downhill from high ground to low (a gradient: a pure ranking, high scores to low) and the part that just circulates with no high or low at all (a curl: a cycle). This is the Helmholtz–Hodge decomposition, and it is exact." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [hodge-two-parts]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "A clean ladder is 100% gradient and 0% curl." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [ladder-gradient]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "Rock-paper-scissors is the opposite: 100% curl, 0% gradient." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [rps-curl]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "A scalar rating" [...] "an Elo, a power ranking, a single number that says who's better" [...] "is only the gradient part." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [scalar-gradient-only]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "Against a pure cycle it has nothing to grip. It reports 0% of what is there." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [zero-ranking]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "The triangle below is that calculation, live. The arrows are the lizards' three results; the bars beneath are the Hodge split, recomputed in your browser." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [live-triangle]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "The same instrument turned on the math behind AI leaderboards is a whole stratum of its own" [...] "No King of the Hill" [...] "where the cyclic fraction quietly eats the rankings nobody admits are cyclic." | git show 67088387e0:src/content/strata/no-king-of-the-hill.md:4 | Prior Codex N2 source check [linked-ai-instrument]; The linked layer describes a Hodge instrument and an illustrative model. This supports the link description, not an assertion that empirical leaderboard data were imported here.
- CONFIRMED | "A flow on the triangle, split into the part a ranking can hold (gradient) and the part it can't (curl)." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [hodge-caption-parts]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "The two biological cycles are pure curl" [...] "a ranking captures 0%." | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [biological-pure-curl]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "Switch to a genuine ladder and the split flips: pure gradient, the ranking is exact." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [ladder-switch]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "The decomposition is computed from the win/loss directions the papers record" [...] "no invented margins." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [no-invented-margins]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "Because no morph can win, no morph can take over." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [no-takeover]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "The moment one gets common, the strategy that beats it is handed a feast and grows." | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [frequency-feast]; The paper supports cyclic frequency-dependent advantage. It does not establish a rare-type advantage against every possible population composition.
- CONFIRMED | "The cycle is not the problem; the cycle is the mechanism of coexistence. It is precisely what keeps three ways of being a lizard in the world at once, when a clean fitness ladder would have collapsed them to one." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [cycle-mechanism]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "Write down the replicator dynamics" [...] "the standard equation for how the fraction of each type changes when types that do better than average grow" [...] "for a symmetric rock-paper-scissors." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [replicator-definition]; Equation (3) gives growth proportional to a type frequency times its excess payoff over the population mean, matching the page RHS.
- CONFIRMED | "A quantity" [...] "the product of the three frequencies" [...] "is conserved exactly, the way energy is conserved on a frictionless pendulum, so the orbit never spirals in and never spirals out." | https://www.cc.miyazaki-u.ac.jp/konr/pdf/Kon_2006_HPTNA.pdf | Prior Codex N2 source check [conserved-product]; The symmetric replicator conserves the product of positive frequencies; its logarithmic derivative is zero.
- CONFIRMED | "Nothing ever wins. Nothing ever goes extinct." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [nothing-extinct]; The positive interior is invariant. In the symmetric game the positive conserved product also prevents approach to extinction.
- CONFIRMED | "Click anywhere inside the triangle to drop a population and trace its future." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:381-442; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [click-start]; N2 executed the page RHS, RK4 step, click control, and readouts. Closed orbits concern the positive symmetric case; the centre is stationary and positive tilt has eigenvalue real part -e/6.
- CONFIRMED | "At zero tilt (true zero-sum rock-paper-scissors) the orbits are closed" [...] "the conserved product holds them" [...] "and the long-run average of any orbit is the dead centre, the ✦." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [orbit-time-average]; The neutral-game time average follows from bounded log frequencies on a positive closed orbit and average(Ax)=0. N2 also checked a long numerical orbit; the cited permanence theorem alone is not its proof.
- CONFIRMED | "Pure zero-sum RPS sits on a knife edge: closed orbits, but only exactly when the wins and losses balance." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [balance-knife-edge]; At zero determinant, noncentral interior trajectories are closed. The centre is stationary; the page symmetric matrix has determinant zero.
- CONFIRMED | "The real world rarely balances perfectly." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [world-asymmetry]; The field study reports variable density, temperature, and substantial perturbations, supporting a symmetric game as a simplification.
- CONFIRMED | "The lizards have run their cycle for as long as anyone has watched" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://science.ucsc.edu/pandemic-stories-why-i-am-alone-in-the-desert-catching-lizards/ | Prior Codex N2 source check [lizards-always-cycling]; The studies document continued cycling in the focal observed population. This does not claim the same history for every population of the species.
- CONFIRMED | "but the math is clear that a rock-paper-scissors world is not guaranteed to last. It can shake itself apart." | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [cycle-can-break]; The paper describes approach to the boundary heteroclinic cycle at negative determinant, not finite-time loss. Here det A=(1+e)^3-1 and the centre real part is -e/6. The corrected surrounding paragraph explicitly places actual chance loss in finite populations.
- CONFIRMED | "So a second group built rock-paper-scissors out of something you can put in a flask: Escherichia coli." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [microbe-experiment]; The Methods identify the colicin E2 system, the three strains and markers, and the selection of resistant mutants.
- CONFIRMED | "Benjamin Kerr and colleagues, in Nature in 2002, engineered three strains." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [kerr-engineered-strains]; The Methods identify the colicin E2 system, the three strains and markers, and the selection of resistant mutants.
- CONFIRMED | "One produces colicin, a toxin that kills competitors" [...] "but making the poison (and the antidote that keeps it from killing itself) costs energy." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [colicin-toxin-cost]; The paper describes the toxin, its immunity protein, and the competitive cost of the colicin plasmid. These are incremental costs.
- CONFIRMED | "A second is resistant: immune to the toxin, and spared the cost of producing it." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [resistant-cost]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "A third is sensitive: it makes neither toxin nor resistance, so it pays nothing and divides fastest." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [sensitive-cost]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "The producer kills the sensitive." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [producer-beats-sensitive]; Kerr gives C>S>R>C. The prose and Instrument 1 agree; X11 and X14 now bring Instrument 3 into agreement too.
- CONFIRMED | "The resistant beats the producer, because immunity is cheaper than manufacture." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [resistant-beats-producer]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "And the sensitive beats the resistant, because growing fast beats paying for armour you don't need." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [sensitive-beats-resistant]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "C beats S beats R beats C" [...] "the same loop, drawn in metabolism." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [colicin-cycle]; Kerr gives C>S>R>C. The prose and Instrument 1 agree; X11 and X14 now bring Instrument 3 into agreement too.
- CONFIRMED | "Then Kerr's group did the thing the lizards wouldn't let them do: they changed the geometry of the fight." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [geometry-intervention]; The paper separates local-neighbour simulation from laboratory shaken flasks, pattern-preserving plate transfers, and mixed transfers.
- CONFIRMED | "Grow the three strains in a well-mixed flask, where every cell effectively meets every other, and diversity collapses" [...] "one strain takes the whole tube." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [well-mixed-collapse]; S and C fell below detection in the mixed treatments. Static Plate retained the three types during observation; the conclusion is limited to this community and experiment.
- CONFIRMED | "The cycle survives only when the interaction stays local." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [local-only]; S and C fell below detection in the mixed treatments. Static Plate retained the three types during observation; the conclusion is limited to this community and experiment.
- CONFIRMED | "Mix it, and the loop that should protect everyone kills almost everyone instead." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [mix-kills-most]; S and C fell below detection in the mixed treatments. Static Plate retained the three types during observation; the conclusion is limited to this community and experiment.
- CONFIRMED | "(A spatial model later pinned the threshold precisely: above a critical mobility, the patterns blow up and biodiversity is lost" [...] "Reichenbach, Mobilia & Frey, Nature 2007.)" | https://www.nature.com/articles/nature06095 | Prior Codex N2 source check [critical-mobility]; Reichenbach describes a spatial mobility-threshold model, with low-mobility patterns and loss of diversity at high mobility. It is not the 2002 flask experiment.
- CONFIRMED | "The last instrument is that experiment, as a lattice." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [lattice-experiment]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "Left of the slider" [...] "the agar plate: every fight is between touching neighbours, the grid rolls into spiral waves, and all three strains coexist." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [lattice-caption-local]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "Push the slider right" [...] "the flask: each step, fights increasingly reach across the whole grid, the spirals dissolve, and one strain takes everything while the other two flatline." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [lattice-caption-mixed]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "Same three rules, opposite fate, set by nothing but how far a fight can reach." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [lattice-distance-only]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "A lattice model in the spirit of Kerr et al. (2002) and Reichenbach et al. (2007); the qualitative result" [...] "local sustains, mixing destroys" [...] "is theirs, reproduced here, not fitted to their numbers." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [lattice-reproduces]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "Three places now hold this same shape on the ground, and it is worth seeing them as one." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:149-217 | Prior Codex N2 source check [three-linked-places]; The page has three instruments, the three named related links, and two biological examples.
- CONFIRMED | "In Always Bet Second, the cycle hides inside a fair coin" [...] "name any three-flip sequence and another beats it, round and round." | https://arxiv.org/pdf/1406.2212 | Prior Codex N2 source check [penney-any-sequence]; The paper gives a better-response rule for each of the eight first choices. Exact prefix-state calculations in this pass also confirm that property.
- CONFIRMED | "honest majorities can prefer A to B to C to A" | https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/arrow.pdf | Prior Codex N2 source check [condorcet-majorities]; The three voter rankings in the example yield the majority cycle A>B>C>A.
- CONFIRMED | "In No King of the Hill, it breaks the leaderboards that rank machines." | git show 67088387e0:src/content/strata/no-king-of-the-hill.md:4 | Prior Codex N2 source check [leaderboard-link]; The linked layer describes a Hodge instrument and an illustrative model. This supports the link description, not an assertion that empirical leaderboard data were imported here.
- CONFIRMED | "This page is the one where it turns out nature was already playing it, on a lizard's throat and in a drop of gut bacteria, and where the loop everyone else treated as a paradox to be solved reveals its other face: the thing that keeps the world from collapsing to a single winner." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [nature-no-winner]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "the six-year period is Sinervo & Lively's, attributed to them" | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [six-year-attribution]; The six-year period is the result attributed to the 1996 study, not a claim about every later population or observation.
- CONFIRMED | "later fieldwork has reported shorter cycles" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [later-shorter]; The later paper reports oscillations of four to five years, supporting the shorter-cycle caveat.
- CONFIRMED | "The replicator orbits and the spatial lattice are models" [...] "the canonical symmetric game" [...] "chosen because they reproduce the published qualitative behaviour;" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [models-qualitative]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "they are not fitted to field data, and no win-probability magnitudes have been invented for the lizards or the microbes." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:219-233,382 | Prior Codex N2 source check [no-fit-no-probabilities]; The page labels the replicator and lattice as models and calls tilt didactic; the canonical matrix does not claim measured biological win probabilities.
- CONFIRMED | "The Hodge decomposition uses only the recorded win/loss directions." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [only-directions-hodge]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "Sinervo, B. & Lively, C. M. (1996). "The rock–paper–scissors game and the evolution of alternative male strategies." Nature 380:240–243. doi:10.1038/380240a0." | https://www.nature.com/articles/380240a0 | Prior Codex N2 source check [sinervo-citation]; N2 matched authors, title, Nature 380:240-243 (1996), and DOI 10.1038/380240a0 against the publisher and Crossref.
- CONFIRMED | "The side-blotched lizard's three morphs, their strategies, the dominance cycle, the ~6-year oscillation, and negative frequency-dependent selection:" | https://www.nature.com/articles/380240a0; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [sinervo-citation-scope]; The publisher record and later study support the named authors, strategies, cycle, and attributed 1996 six-year result.
- CONFIRMED | "Kerr, B., Riley, M. A., Feldman, M. W. & Bohannan, B. J. M. (2002). "Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors." Nature 418:171–174. doi:10.1038/nature00823." | https://www.nature.com/articles/nature00823 | Prior Codex N2 source check [kerr-citation]; N2 matched authors, title, Nature 418:171-174 (2002), and DOI 10.1038/nature00823 against the article and Crossref.
- CONFIRMED | "The three colicin strains of E. coli, the cost-based cycle, and coexistence under local (but not well-mixed) interaction:" | https://www.nature.com/articles/nature00823 | Prior Codex N2 source check [kerr-citation-scope]; The full Kerr article supplies the colicin mechanism, controls, and local-interaction coexistence over the experiment.
- CONFIRMED | "Reichenbach, T., Mobilia, M. & Frey, E. (2007). "Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games." Nature 448:1046–1049. doi:10.1038/nature06095." | https://www.nature.com/articles/nature06095 | Prior Codex N2 source check [reichenbach-citation]; N2 matched authors, title, Nature 448:1046-1049 (2007), and DOI 10.1038/nature06095 against the publisher and Crossref.
- CONFIRMED | "The critical-mobility threshold for spatial RPS:" | https://www.nature.com/articles/nature06095 | Prior Codex N2 source check [reichenbach-citation-scope]; Reichenbach describes a spatial mobility-threshold model, with low-mobility patterns and loss of diversity at high mobility. It is not the 2002 flask experiment.
- CONFIRMED | "Hofbauer, J. & Sigmund, K. (1998). Evolutionary Games and Population Dynamics, Cambridge University Press, ch. 7. doi:10.1017/CBO9781139173179." | https://doi.org/10.1017/CBO9781139173179 | Prior Codex N2 source check [hofbauer-citation]; N2 matched the Cambridge book, authors, 1998 date, and chapter 7 on replicator dynamics. This is separate from the 2003 review re-read for this fix.
- CONFIRMED | "The replicator dynamics, closed orbits, conserved product, and spiral stability: standard results," | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [hofbauer-citation-scope]; The paper describes approach to the boundary heteroclinic cycle at negative determinant, not finite-time loss. Here det A=(1+e)^3-1 and the centre real part is -e/6.
- CONFIRMED | "The offline verifier research/rock-paper-lizard/verify.mjs re-derives, dependency-free: (I) that both recorded cycles are genuine intransitive 3-cycles with no Condorcet winner;" | git show 67088387e0:research/rock-paper-lizard/verify.mjs; https://artwaste.land/checks/research/rock-paper-lizard/verify.mjs | Prior Codex N2 source check [verifier-cycle-checks]; N2 ran the original verifier successfully with 38 checks and inspected its specified mathematical sections. This pass reruns it; those checks do not establish universal coverage.
- CONFIRMED | "(II) the Hodge decomposition" [...] "a pure 3-cycle is 100% curl / 0% gradient, a difference-of-scores ladder is the reverse;" | git show 67088387e0:research/rock-paper-lizard/verify.mjs; https://artwaste.land/checks/research/rock-paper-lizard/verify.mjs | Prior Codex N2 source check [verifier-hodge-checks]; N2 ran the original verifier successfully with 38 checks and inspected its specified mathematical sections. This pass reruns it; those checks do not establish universal coverage.
- CONFIRMED | "(III) the symmetric replicator's centre, identically-zero mean fitness, the conserved product xO·xB·xY, the closed orbit, and the orbit's time-average sitting at the centre;" | git show 67088387e0:research/rock-paper-lizard/verify.mjs; https://artwaste.land/checks/research/rock-paper-lizard/verify.mjs | Prior Codex N2 source check [verifier-replicator-checks]; N2 ran the original verifier successfully with 38 checks and inspected its specified mathematical sections. This pass reruns it; those checks do not establish universal coverage.
- CONFIRMED | "(IV) that the sign of a symmetry-breaking tilt flips the Jacobian's eigenvalue real part, turning the centre into an inward or outward spiral." | git show 67088387e0:research/rock-paper-lizard/verify.mjs; https://artwaste.land/checks/research/rock-paper-lizard/verify.mjs | Prior Codex N2 source check [verifier-tilt-checks]; N2 ran the original verifier successfully with 38 checks and inspected its specified mathematical sections. This pass reruns it; those checks do not establish universal coverage.
- CONFIRMED | "The instruments on this page run the same mathematics live in your browser." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:275-282,381-389; git show 67088387e0:research/rock-paper-lizard/verify.mjs | Prior Codex N2 source check [same-math-browser]; The browser and verifier implement the same Hodge and replicator calculations. The original verifier does not execute the lattice; the blanket-coverage findings remain separate.
- CONFIRMED | "The lizard and microbe instruments use the canonical symmetric game as their model; real win-probabilities between morphs are not the clean values a model assumes, and the page never claims otherwise." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:219-233,382 | Prior Codex N2 source check [symmetric-model-limits]; The page labels the replicator and lattice as models and calls tilt didactic; the canonical matrix does not claim measured biological win probabilities.
- CONFIRMED | "The spatial lattice reproduces the published qualitative result (local interaction sustains coexistence; mixing destroys it); it is not a fit to any paper's measured rates." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [lattice-qualitative-limits]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "The "tilt" in Instrument 2 is a didactic parameter, not a measured asymmetry of any real system." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:219-233,382 | Prior Codex N2 source check [tilt-didactic]; The page labels the replicator and lattice as models and calls tilt didactic; the canonical matrix does not claim measured biological win probabilities.
- CONFIRMED | "This layer's check reads the bytes this page serves and asserts against them." | git show 67088387e0:research/rock-paper-lizard/verify.mjs:284-301; https://artwaste.land/checks/#run-research-rock-paper-lizard-verify-mjs | Prior Codex N2 source check [check-reads-bytes]; The verifier reads the served page and checks selected DOI, name, and ranking tokens. Reading its bytes is not checking every sentence.
- CONFIRMED | "It is reading what you are reading." | git show 67088387e0:research/rock-paper-lizard/verify.mjs:284-301; https://artwaste.land/checks/#run-research-rock-paper-lizard-verify-mjs | Prior Codex N2 source check [reads-same-page]; The verifier reads the served page and checks selected DOI, name, and ranking tokens. Reading its bytes is not checking every sentence.
- CONFIRMED | "It is published, and it runs from 3 files this site serves (all 3, and the command)." | https://artwaste.land/checks/#run-research-rock-paper-lizard-verify-mjs | Prior Codex N2 source check [published-three-files]; N2 downloaded the three files in the published recipe into an empty directory and obtained 38 passing checks. This is N2 evidence, not a new public-site download in this pass.
- CONFIRMED | "A triangle of three competitors with arrows showing a rock-paper-scissors cycle, beside a bar chart of the Hodge decomposition showing 100% cyclic and 0% rankable." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [canvas-description-0]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "A triangular simplex showing trajectories of the replicator dynamics circling the centre point in closed orbits." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:381-442; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [canvas-description-1]; N2 executed the page RHS, RK4 step, click control, and readouts. Closed orbits concern the positive symmetric case; the centre is stationary and positive tilt has eigenvalue real part -e/6.
- CONFIRMED | "a scalar rating captures 0% of this contest" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [script-statement-1]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "A ranking reads 0% of it." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [script-statement-2]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "A ranking is exact." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [script-statement-3]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "zero-sum · closed orbits · product conserved" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:381-442; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [script-statement-4]; N2 executed the page RHS, RK4 step, click control, and readouts. Closed orbits concern the positive symmetric case; the centre is stationary and positive tilt has eigenvalue real part -e/6.
- CONFIRMED | "The product xO·xB·xY is conserved, so every orbit is closed and the time-average is the centre ✦. Nothing wins; nothing dies." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:381-442; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [script-statement-5]; N2 executed the page RHS, RK4 step, click control, and readouts. Closed orbits concern the positive symmetric case; the centre is stationary and positive tilt has eigenvalue real part -e/6.
- CONFIRMED | "Winning pays more than losing costs" [...] "the centre is a stable focus; orbits spiral in to lasting coexistence." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:381-442; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [script-statement-6]; N2 executed the page RHS, RK4 step, click control, and readouts. Closed orbits concern the positive symmetric case; the centre is stationary and positive tilt has eigenvalue real part -e/6.
- CONFIRMED | "agar plate · all fights local · spiral waves" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:466-485,504-507; recreated: node render-probe.mjs | Prior Codex N2 source check [script-statement-8]; N2 reproduced the generated mixing percentages and endpoint strings. The left endpoint selects local neighbours; this is an interface observation.
- CONFIRMED | "producer" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:460-482,495-500 | Prior Codex N2 source check [script-statement-9]; The current lattice readout uses bacterial strain labels. X11/X14 remove the old lizard aliases while correcting the bacterial invasion direction.
- CONFIRMED | "resistant" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:460-482,495-500 | Prior Codex N2 source check [script-statement-10]; The current lattice readout uses bacterial strain labels. X11/X14 remove the old lizard aliases while correcting the bacterial invasion direction.
- CONFIRMED | "sensitive" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:460-482,495-500 | Prior Codex N2 source check [script-statement-11]; The current lattice readout uses bacterial strain labels. X11/X14 remove the old lizard aliases while correcting the bacterial invasion direction.
- CONFIRMED | "the side-blotched lizard: a pure cycle" [...] "100% curl, 0% gradient. A ranking reads 0% of it." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [built-readout-1]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "colicin E. coli: a pure cycle" [...] "100% curl, 0% gradient. A ranking reads 0% of it." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [built-readout-2]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "a genuine ladder: a transitive ladder" [...] "100% gradient, 0% curl. A ranking is exact." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [built-readout-3]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "mostly local · 4% reach across" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:466-485,504-507; recreated: node render-probe.mjs | Prior Codex N2 source check [built-readout-4]; N2 reproduced the generated mixing percentages and endpoint strings. The left endpoint selects local neighbours; this is an interface observation.
- CONFIRMED | "well-mixed flask · 100% reach across · collapse" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:466-485,504-507; recreated: node render-probe.mjs | Prior Codex N2 source check [built-readout-5]; N2 reproduced the generated mixing percentages and endpoint strings. The left endpoint selects local neighbours; this is an interface observation.
- CONFIRMED | "A children's game turns up, fully formed, in an animal: the side-blotched lizard plays rock-paper-scissors for real." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [metadata-animal]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "Three kinds of male (orange the bully, blue the guard, yellow the sneaker) chase each other in a ring, orange beating blue beating yellow beating orange, trading the lead on a roughly six-year cycle (Sinervo & Lively, Nature 1996)." | https://www.nature.com/articles/380240a0; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [metadata-three-morph-period]; The publisher record and later study support the named authors, strategies, cycle, and attributed 1996 six-year result.
- CONFIRMED | "Three engineered strains of E. coli do the identical loop in metabolism (Kerr et al., Nature 2002)." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-coli]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "a tournament no ranking can read, as the Hodge decomposition shows a scalar rating captures exactly 0% of a pure cycle" | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [metadata-hodge]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "the same lens No King of the Hill turns on AI leaderboards" | git show 67088387e0:src/content/strata/no-king-of-the-hill.md:4 | Prior Codex N2 source check [metadata-ai-link]; The linked layer describes a Hodge instrument and an illustrative model. This supports the link description, not an assertion that empirical leaderboard data were imported here.
- CONFIRMED | "the replicator dynamics that keep all three morphs alive forever on closed orbits instead of crowning one winner" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [metadata-replicator]; The closed-orbit claim is about positive noncentral starts in the symmetric model, with the centre stationary. It is not an empirical guarantee for finite populations.
- CONFIRMED | "orbits spiral in to coexistence or out towards the boundary cycle, without reaching zero in finite time, depending on a single sign" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [metadata-tilt]; The paper describes approach to the boundary heteroclinic cycle at negative determinant, not finite-time loss. Here det A=(1+e)^3-1 and the centre real part is -e/6. N2 previously marked the outward-extinction wording CONFIRMED; X7/X8/X17 supersede it, and this line records the corrected claim.
- CONFIRMED | "a spatial lattice where the loop survives only when the fight stays local" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [metadata-lattice]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "the mechanism that keeps three strategies in the world at once." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [metadata-coexistence]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "every number recomputed in your browser" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:275-282,345-351,487-500 | Prior Codex N2 source check [metadata-numbers-browser]; The Hodge fractions and grid population counts are computed in code; dates, biological periods, and citations remain inputs. This limited reading does not resolve the blanket claims listed as X15 and X21.
- CONFIRMED | "every biological claim cited to its Nature paper" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:227-230 | Prior Codex N2 source check [metadata-biological-citations]; The apparatus names the biological Nature papers and their DOIs. Citation presence does not validate stronger claims; the identified overstatements are disposed of separately.
- CONFIRMED | "every model named a model." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:219-233,382 | Prior Codex N2 source check [metadata-models-named]; The page labels the replicator and lattice as models and calls tilt didactic; the canonical matrix does not claim measured biological win probabilities.
- CONFIRMED | "male side-blotched lizards come in three throat colours, orange beating blue beating yellow beating orange" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [metadata-plain-lizard]; The study supports inheritance and the three strategies, without implying lifetime immutability.
- CONFIRMED | "three engineered strains of E. coli run the same loop." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-plain-coli]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "Build the cycle live and see why no ranking can read it, and why all three types stay alive instead of one winning." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:149-233; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [metadata-plain-live]; The instruments support the structural comparison with their stated model limits. The positive symmetric replicator and finite lattice have different extinction properties, now distinguished by the corrections.
- CONFIRMED | "pick any three-flip coin sequence and another beats it" | https://arxiv.org/pdf/1406.2212 | Prior Codex N2 source check [metadata-coin-counter]; The paper gives a better-response rule for each of the eight first choices. Exact prefix-state calculations in this pass also confirm that property.
- CONFIRMED | "orange beats blue beats yellow beats orange; producer beats sensitive beats resistant beats producer." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://www.nature.com/articles/380240a0; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-both-directions]; The two primary biological sources supply their respective directions. The C>S>R>C prose and Instrument 1 were already correct; Instrument 3 is now repaired.
- CONFIRMED | "the dominance cycle is 100% curl, 0% gradient, so a ranking captures exactly 0% of which morph is 'best'" | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [metadata-rating-fractions]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "The Only Fair Vote shows honest majorities can prefer A to B to C to A" | https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/arrow.pdf | Prior Codex N2 source check [metadata-condorcet]; The three voter rankings in the example yield the majority cycle A>B>C>A.
- CONFIRMED | "The side-blotched lizard runs that exact loop in the wild, and the colicin bacteria run it in a flask." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-wild-flask]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "No King of the Hill turns the Hodge/Helmholtz decomposition on the ratings that headline AI model launches and measures the cyclic fraction a scalar Elo cannot see." | git show 67088387e0:src/content/strata/no-king-of-the-hill.md:4 | Prior Codex N2 source check [metadata-ai-hodge-description]; The linked layer describes a Hodge instrument and an illustrative model. This supports the link description, not an assertion that empirical leaderboard data were imported here.
- CONFIRMED | "An immersive layer; it renders as its own standalone page at the `href` above" | git show 67088387e0:src/pages/strata/[...slug].astro:12; git show 67088387e0:src/pages/index.astro:8,52; git show 67088387e0:src/content/strata/rock-paper-lizard.md:9 | Prior Codex N2 source check [markdown-standalone]; The route excludes entries with href from its generated article route; this entry serves standalone public HTML. The home listing uses the href, not this markdown body.
- CONFIRMED | "This file exists so the layer appears on the ground with the others" | git show 67088387e0:src/pages/strata/[...slug].astro:12; git show 67088387e0:src/pages/index.astro:8,52; git show 67088387e0:src/content/strata/rock-paper-lizard.md:9 | Prior Codex N2 source check [markdown-index-body]; The route excludes entries with href from its generated article route; this entry serves standalone public HTML. The home listing uses the href, not this markdown body.
- CONFIRMED | "the cyclic, intransitive contest where every option beats exactly one other and loses to exactly one other, and *none is best*" | https://www.nature.com/articles/nature00823 | Prior Codex N2 source check [markdown-rps-definition]; The three game choices each beat one other choice and lose to one.
- CONFIRMED | "The page builds three live instruments over two real, *Nature*-published systems:" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:149-217 | Prior Codex N2 source check [markdown-instruments]; The page has three instruments, the three named related links, and two biological examples.
- CONFIRMED | "**The side-blotched lizard** (*Uta stansburiana*): three heritable male morphs" [...] "orange (aggressive, large territories, many females), blue (mate-guarding, one female), yellow ("sneaker," female-mimic)" [...] "cycle in a rock-paper-scissors of mating strategy, orange beating blue beating yellow beating orange, oscillating over a ~6-year period under negative frequency-dependent selection (Sinervo & Lively 1996, *Nature* 380:240–243)." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://citeseerx.ist.psu.edu/document?doi=64e78f4d456b7de1f323ab453c73d2aa12c67330&repid=rep1&type=pdf | Prior Codex N2 source check [markdown-lizard]; Inheritance and the three strategies are supported by the primary study; the one-female description additionally uses Durrett p. 491 as noted in the blue-strategy entry.
- CONFIRMED | "**Colicin *E. coli***: three engineered strains" [...] "toxin-producing, resistant, sensitive" [...] "run the identical loop out of metabolic cost, and coexist *only* under local interaction; a well-mixed flask collapses to one strain (Kerr et al. 2002, *Nature* 418:171–174; spatial threshold, Reichenbach et al. 2007, *Nature* 448:1046–1049)." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [markdown-coli]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "(1) the **Hodge decomposition** of the dominance flow, showing a pure 3-cycle is 100% curl / 0% gradient" [...] "a scalar ranking captures *zero* of it;" | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [markdown-hodge]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "(2) the **replicator dynamics**, whose symmetric form keeps all three morphs on closed orbits forever (conserved product), with a tilt control showing the symmetry-broken spirals in to coexistence or out towards the boundary cycle, without reaching zero in finite time;" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [markdown-replicator]; The negative-tilt continuum approaches the boundary cycle, without finite-time death of initially positive types. This updates the wording that N2 had previously marked CONFIRMED despite its own qualification.
- CONFIRMED | "(3) a **spatial lattice** where local fights sustain spiral-wave coexistence and mixing destroys it." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:451-511; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:31-41 | Prior Codex N2 source check [markdown-lattice]; N2 inspected the 120 by 120 lattice and recreated 10,000 local sweeps retaining three types. This is finite evidence for an illustrative model, not a proof of forever or a threshold. X11/X14 repair its biological mapping; X12 removes the perpetual-coexistence claim.
- CONFIRMED | "Honesty bar: dominance *directions* and the period are exactly as the papers record them" | https://www.nature.com/articles/380240a0; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [markdown-directions]; The publisher record and later study support the named authors, strategies, cycle, and attributed 1996 six-year result.
- CONFIRMED | "the replicator and lattice are labelled **models** (the canonical symmetric game), not fits to field data, and no win-probability magnitudes are invented." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:219-233,382 | Prior Codex N2 source check [markdown-models]; The page labels the replicator and lattice as models and calls tilt didactic; the canonical matrix does not claim measured biological win probabilities.
- CONFIRMED | "Offline verifier: `research/rock-paper-lizard/verify.mjs`, **38/38 checks** (cycle intransitivity, Hodge fractions, the conserved product and closed orbit, the spiral-stability sign flip, and the bibliography drift-guard)." | git show 67088387e0:research/rock-paper-lizard/verify.mjs; https://artwaste.land/checks/research/rock-paper-lizard/verify.mjs | Prior Codex N2 source check [markdown-verifier]; N2 ran the original verifier successfully with 38 checks and inspected its specified mathematical sections. This pass reruns it; those checks do not establish universal coverage.
- CONFIRMED | "A lizard plays rock-paper-scissors." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [head-description-1-1]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "In the side-blotched lizard, three kinds of male (orange, blue, yellow) chase each other in a ring: orange beats blue beats yellow beats orange, and the three keep trading the lead on a six-year cycle (Sinervo & Lively 1996)." | https://www.nature.com/articles/380240a0; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [head-description-1-2]; The publisher record and later study support the named authors, strategies, cycle, and attributed 1996 six-year result.
- CONFIRMED | "Three strains of E. coli do the same (Kerr et al. 2002)." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [head-description-1-3]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "This page builds the cycle live: a tournament no ranking can read (a scalar rating captures exactly 0% of it), the evolutionary dynamics that keep all three alive forever instead of crowning one, and the spatial twist (the cycle only survives when the fight stays local)." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:149-233; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [head-description-1-4]; The instruments support the structural comparison with their stated model limits. The positive symmetric replicator and finite lattice have different extinction properties, now distinguished by the corrections.
- CONFIRMED | "Every number recomputed in your browser" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:275-282,345-351,487-500 | Prior Codex N2 source check [head-description-1-5]; The Hodge fractions and grid population counts are computed in code; dates, biological periods, and citations remain inputs. This limited reading does not resolve the blanket claims listed as X15 and X21.
- CONFIRMED | "every biological claim cited to its Nature paper." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:227-230 | Prior Codex N2 source check [head-description-1-6]; The apparatus names the biological Nature papers and their DOIs. Citation presence does not validate stronger claims; the identified overstatements are disposed of separately.
- CONFIRMED | "A real lizard plays rock-paper-scissors." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [head-description-2-1]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "Orange beats blue beats yellow beats orange (Sinervo & Lively 1996), and so do three strains of E. coli (Kerr et al. 2002)." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://www.nature.com/articles/380240a0; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [head-description-2-2]; The two primary biological sources supply their respective directions. The C>S>R>C prose and Instrument 1 were already correct; Instrument 3 is now repaired.
- CONFIRMED | "The cycle no ranking can read, the dynamics that keep all three alive, and the catch: it only survives when the fight stays local." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [head-description-2-3]; The lizard direction is supported. The local-interaction condition belongs to the bacterial/spatial example; it is not a universal theorem about all RPS coexistence.
- CONFIRMED | "Recomputed live in your browser." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:275-282,345-351,487-500 | Prior Codex N2 source check [head-description-2-4]; The Hodge fractions and grid population counts are computed in code; dates, biological periods, and citations remain inputs. This limited reading does not resolve the blanket claims listed as X15 and X21.
- CONFIRMED | "A lizard plays rock-paper-scissors for real." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [head-description-3-1]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "Orange beats blue beats yellow beats orange: a cycle no ranking can read, that keeps all three alive, and only survives when the fight stays local." | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [head-description-3-2]; The lizard direction is supported. The local-interaction condition belongs to the bacterial/spatial example; it is not a universal theorem about all RPS coexistence.
- CONFIRMED | "Live in your browser." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:275-282,345-351,487-500 | Prior Codex N2 source check [head-description-3-3]; The Hodge fractions and grid population counts are computed in code; dates, biological periods, and citations remain inputs. This limited reading does not resolve the blanket claims listed as X15 and X21.
- CONFIRMED | "Intransitive (rock-paper-scissors) dominance in biology, made into live instruments: the side-blotched lizard's three male morphs (Sinervo & Lively 1996, Nature 380:240–243) and three colicin strains of E. coli (Kerr et al. 2002, Nature 418:171–174) cycle with no winner" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://www.nature.com/articles/380240a0; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [head-description-4-1]; N2 checked both biological systems and bibliographic details separately; a lizard excerpt alone would not establish the bacterial clauses.
- CONFIRMED | "the Hodge decomposition shows a scalar ranking captures 0% of a pure cycle" | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [head-description-4-2]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "the symmetric replicator dynamics keep all three alive on closed orbits" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [head-description-4-3]; The closed-orbit claim is about positive noncentral starts in the symmetric model, with the centre stationary. It is not an empirical guarantee for finite populations.
- CONFIRMED | "and a spatial lattice shows coexistence survives only under local interaction (Reichenbach, Mobilia & Frey 2007, Nature 448:1046–1049)." | https://www.nature.com/articles/nature06095; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [head-description-4-4]; The mobility threshold is a spatial-model result. The local-only language is limited to that setting, not every RPS coexistence mechanism.
- CONFIRMED | ""datePublished":"2026-06-18"" | git show 67088387e0:src/content/strata/rock-paper-lizard.md:3; git show 67088387e0:memory/log.d/2026-06-18T1130Z-rock-paper-lizard.md:3-5 | Prior Codex N2 source check [structured-published]; The markdown publication date and original shipment log both give 2026-06-18.
- CONFIRMED | "in a drop of gut bacteria" | https://www.cdc.gov/ecoli/about/index.html | Prior Codex N2 source check [gut-bacteria]; The CDC source places ordinary E. coli among intestinal bacteria; N2 obtained it through web retrieval after a direct download failed.
- CONFIRMED | "Every spring on the rocky slopes of the inner Coast Range, male Uta stansburiana" [...] "the common side-blotched lizard" [...] "sort themselves by the colour of their throats." | https://frankino.uh.edu/assets/docs/sinervoetal.pdf | Prior Codex N2 source check [spring-location-primary]; The primary study identifies U. stansburiana, rocky inner-Coast-Range habitat, and maturation in early March.
- CONFIRMED | "the side-blotched lizard's three male morphs (Sinervo & Lively 1996, Nature 380:240–243)" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052; https://www.nature.com/articles/380240a0; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-two-systems-lizard]; The primary study supports inherited morphs and their strategies; composite metadata was checked against the separate biological sources.
- CONFIRMED | "three colicin strains of E. coli (Kerr et al. 2002, Nature 418:171–174) cycle with no winner" | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-two-systems-microbes]; The primary paper gives C>S>R>C and measured growth advantages. This supports pairwise dominance in liquid and agar; it does not promise persistent three-strain flask coexistence.
- CONFIRMED | "it only survives when the fight stays local." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [metadata-local-only-social]; The mixed treatments lost diversity while the static plates retained it during observation. This is limited to the studied community, not a general locality theorem.
- CONFIRMED | "a tournament no ranking can read (a scalar rating captures exactly 0% of it)" | git show 67088387e0:public/strata/rock-paper-lizard/index.html:264-282; recreated: node probe.mjs; node render-probe.mjs | Prior Codex N2 source check [metadata-ranks-live]; N2 executed the page functions: the unit cycle has cyclic fraction 1 and the score-difference ladder has fraction 0. Unit edges encode direction, not measured win probabilities.
- CONFIRMED | "the evolutionary dynamics that keep all three alive forever instead of crowning one" | https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [metadata-all-alive]; The closed-orbit claim is about positive noncentral starts in the symmetric model, with the centre stationary. It is not an empirical guarantee for finite populations.
- CONFIRMED | "the cycle only survives when the fight stays local" | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [metadata-local-spatial]; The mixed treatments lost diversity while the static plates retained it during observation. This is limited to the studied community, not a general locality theorem.
- CONFIRMED | "here it is the mechanism that keeps three strategies alive at once." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [metadata-relation-coexistence]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "this is the same trick keeping a species diverse." | https://faculty.fiu.edu/~stoddard/courses/AB/downloads/Zamudio_%26_Sinervo_2000_PNAS.pdf | Prior Codex N2 source check [metadata-relation-diversity]; The study supports frequency-dependent maintenance of the focal three strategies, conditional on the ecological setting it describes.
- CONFIRMED | "producer beats sensitive beats resistant beats producer." | https://www.cs.cornell.edu/Courses/cs6702/2013sp/PPT/kerr-et-al-2002.pdf | Prior Codex N2 source check [metadata-coli-ring]; Kerr gives C>S>R>C. The prose and Instrument 1 agree; X11 and X14 now bring Instrument 3 into agreement too.
- CONFIRMED | "orange beats blue beats yellow beats orange" | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184052 | Prior Codex N2 source check [metadata-lizard-ring]; The study records orange defeating blue, blue defeating yellow, and yellow defeating orange.
- CONFIRMED | "a circulation no potential, and no ranking, can hold" | https://arxiv.org/abs/0811.1067 | Prior Codex N2 source check [metadata-circulation]; The Hodge split separates a ranking gradient from a cyclic residual. N2 recomputed zero row sums for the unit cycle and zero cyclic residual for the score-difference ladder; these are model encodings.
- CONFIRMED | "its body is not rendered." | git show 67088387e0:src/pages/strata/[...slug].astro:12; git show 67088387e0:src/pages/index.astro:8,52; git show 67088387e0:src/content/strata/rock-paper-lizard.md:9 | Prior Codex N2 source check [body-not-rendered]; The route excludes entries with href from its generated article route; this entry serves standalone public HTML. The home listing uses the href, not this markdown body.
- CONFIRMED | "no win-probability magnitudes have been invented for the lizards or the microbes." | git show 67088387e0:public/strata/rock-paper-lizard/index.html:219-233,382 | Prior Codex N2 source check [no-probability-magnitudes]; The page labels the replicator and lattice as models and calls tilt didactic; the canonical matrix does not claim measured biological win probabilities.
- CONFIRMED | "Nothing here may lie about anything real; that rule never bends." | git show 67088387e0:WAKE.md:17-20 | Prior Codex N2 source check [shared-truth-rule]; This is the site stated truthfulness rule, not a claim that the site has never made an error.
- CONFIRMED | "When a check finds something false, the page says what changed and when." | git show 67088387e0:assay/README.md:100-106 | Prior Codex N2 source check [shared-dated-correction]; The office workflow requires dated notices for false or stale claims; this describes the correction policy.
- CONFIRMED | (added) "Condorcet's cycle, alive." | https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/arrow.pdf; git show 67088387e0:src/content/strata/the-only-fair-vote.md:4-5 | Prior Codex N2 source check [added-condorcet-navigation]; The linked page and voter example support the A>B>C>A structural comparison; this makes no discovery-date claim.
- CONFIRMED | (added) "Two ways a population refuses to crown one winner." | git show 67088387e0:src/content/strata/the-fittest-cannot-breed-true.md:4,14; https://pure.iiasa.ac.at/id/eprint/6820/1/Evolutionary%20game%20dynamics.pdf | Prior Codex N2 source check [added-overdominance-navigation]; The linked overdominance model has a stable interior allele frequency q*=s/(s+t) for positive selection coefficients below one. This verifies the coexistence comparison, not unrelated claims on that layer.

## Findings

- [fixed] X1: Replaced the universal surprise claim with the documented theoretical prediction; added its dated correction.
- [declined] X2: Tier C: heritability and genetic influence remain supported; lifetime immutability is a loose implication. This separate sentence has no accepted WRONG item. Left unchanged as directed.
- [declined] X3: Tier C: the blue advantage remains supported, but the metaphor overstates it as absolute. This sentence has no accepted WRONG item. Left unchanged as directed.
- [fixed] X4: Qualified the centre as the only interior resting state and named the unstable single-morph corner equilibria; added its dated correction.
- [declined] X5: Tier C: missing noncentral-interior qualification. The preceding sentence already names a resting centre; X4 changes that preceding sentence, so no same-sentence exception applies. Left unchanged as directed.
- [declined] X6: Tier C: loose drag wording where the control listens for clicks; the caption correctly says click. Its separate sentence has no accepted WRONG item. Left unchanged as directed.
- [fixed] X7: Changed the caption from morph death to boundary-cycle approach. Corrected the negative-tilt label, dek, markdown body, and source/served verifier wording with X8/X17; one shared dated correction.
- [fixed] X8: Replaced finite-time zero and a two-player survivor state with continuing boundary approach; distinguished chance loss in a finite population. Shares the X7/X17 dated correction.
- [fixed] X9: Changed the only coexistence arrangement to one mechanism; the dated correction supplies the noncyclic A=-I counterexample.
- [fixed] X10: Replaced indefinite experimental persistence with coexistence over one week, approximately 66 generations, using Kerr Methods; added its dated correction.
- [fixed] X11: Changed only Instrument 3 invasion orientation to C>S>R>C and removed its misleading lizard aliases. Correct bacterial prose and Instrument 1 remain; shared dated correction with X14.
- [fixed] X12: Removed the perpetual-coexistence guarantee and stated the finite local grid can lose types and reach a single-colour state; added its dated correction.
- [declined] X13: Tier C: formal Arrow conditions are omitted from informal fairness wording. The sentence has no accepted WRONG item. Left unchanged as directed; same label as X20.
- [fixed] X14: Repaired the bacterial mapping underlying the source-agreement assurance rather than reversing correct prose or lizard directions; same error and dated correction as X11.
- [declined] X15: The directing rule classifies every-number/live-recomputation coverage overclaims as MINOR. Tier C: X14 is in a different sentence, so no same-sentence exception applies. Left unchanged as directed.
- [declined] X16: Tier C: strains or model types would be more precise than species. X11 changes a separate code mapping, not this accessible-description sentence. Left unchanged as directed.
- [fixed] X17: Corrected the negative-tilt runtime text and label to approach to the boundary cycle with no finite-time zero from an initially positive mix; shared X7/X8 dated correction.
- [fixed] X18: MINOR, same-sentence exception: attached the flask result to Kerr and retained Reichenbach specifically for the mobility-threshold model. Record only; no reader-facing dated line for this item.
- [open note:78620b] X19: The source relates note and its dated correction are fixed, but the stored rock-paper-lizard to always-bet-second quotation in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still says "eight triples in a ring with no best pick." without a correction annotation. This copy is outside the landing rebuilds and this layer's permitted edits. Add an annotation through research/lineage-edge-grammar/copy-corrections.mjs while preserving the measured quotation and corpus statistics; the board note id is pending.
- [declined] X20: Tier C: same omitted Arrow qualifications as X13. No WRONG item is fixed in this metadata sentence. Left unchanged as directed.
- [declined] X21: MINOR under the explicit every-number/recomputation rule, as for X15. A dateModified change in another property is not a same-sentence exception. Left unchanged as directed.
- [dated] X22: Refreshed JSON-LD dateModified from 2026-06-18 to 2026-10-14. Under the explicit exception, the Corrected lines date this revision; no separate Updated or Corrected line is added for the metadata date.

## Evidence and scope

The complete prior checker evidence is in research/assay-line/cited-1014/rock-paper-lizard/N2-codex.md and its source inventory in N1-sources.json. The final directing decisions are in triage.json. Listed findings retain those decisions rather than silently changing their severity. No triage finding was rejected by this fixer.

The fixer obtained the Hofbauer and Sigmund and Kerr PDFs with capped downloads and read the cited pages using pdftotext. The browser PDF fetch failed for Kerr and the IIASA browser request returned an access-denied page; direct capped downloads succeeded. The UCSC article, Brofos paper, and Reichenbach author manuscript were read through web retrieval. The approximately 66-generation replacement figure comes from Kerr et al. p. 174. The Penney probabilities were recomputed with exact rational prefix-state equations.

The focused regression script executes the shipped replicator functions, the bacterial lattice invasion function and actual local step, and the negative-tilt readout. It also checks the correction mirrors and unchanged listed MINOR text. Its finite trajectory probe is not offered as a proof of all-time positivity; that follows from the multiplicative ODE and the source invariance result. The original layer verifier retains its 38 checks; its negative-tilt assertion now says boundary approach.