Pith Number

pith:UPPIADBJ

pith:2026:UPPIADBJO5GQU3YQZJ2LZGICU3

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A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$

Bin Yi, Hongju (Daisy) Chen, Zhanshan (Sam) Ma

The replicator equation on the simplex has a unique interior fixed point if and only if its payoff matrix satisfies explicit algebraic conditions.

arxiv:2605.13883 v1 · 2026-05-11 · q-bio.PE · cs.GT · cs.MA

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Record completeness

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4 Citations open

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Claims

C1strongest claim

The sufficient and necessary conditions of the replication dynamics equation with a unique fixed point in the interior of simplex S_n for n greater than or equal to 2 are presented.

C2weakest assumption

That the standard form of the replicator equation on the simplex admits a clean algebraic characterization of unique interior fixed points without additional restrictions on the payoff structure or higher-order terms.

C3one line summary

The paper gives necessary and sufficient conditions for the replicator dynamics to possess a unique interior fixed point in the simplex S_n for all n greater than or equal to 2.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] When 𝑛=2, there are four possible types of replication dynamics 2015

[2] Note: (1) for case 1 and 2, there is no fixed point in 𝐼𝑛𝑡S9, and all the orbits tend to 𝐵𝑑S9 1983

[3] However, for this solution to be in Int𝑆., we must have 𝑥,=_`×ab=_`×a_`×a`acd>0,𝑖=1,2,…,𝑁 1998

[4] That is, any orbits except 𝑥≡𝑥∗, we obtain 𝑉𝑥=𝑥,∗pa∗− 1973

[5] Therefore, the payoff matrix of the Hawk-dove game can be derived as follows: 15 A=𝑏−𝑐2𝑏0𝑏2 where 𝑅6=𝐻, 𝑅9=𝐷, are the hawk strategy and dove strategy respectively 1982

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:19.161825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3de800c29774d0a6f10ca74bc9902a6e5b1b447abe7410fafeedcf6346be786

Aliases

arxiv: 2605.13883 · arxiv_version: 2605.13883v1 · doi: 10.48550/arxiv.2605.13883 · pith_short_12: UPPIADBJO5GQ · pith_short_16: UPPIADBJO5GQU3YQ · pith_short_8: UPPIADBJ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UPPIADBJO5GQU3YQZJ2LZGICU3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a3de800c29774d0a6f10ca74bc9902a6e5b1b447abe7410fafeedcf6346be786

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4120b0791de2fa4017d2430b3f876d5ceaf79c0d56f78114a299468512d8c72",
    "cross_cats_sorted": [
      "cs.GT",
      "cs.MA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2026-05-11T14:13:48Z",
    "title_canon_sha256": "f2096faa6858d320153597ff2497db998973d18dfa89561607dd69b1d58396ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13883",
    "kind": "arxiv",
    "version": 1
  }
}