Pith Number

pith:HNPWWAJF

pith:2026:HNPWWAJFFRFILH7OGJXPOJCKN4

not attested not anchored not stored refs resolved

Eventual sign coherence

Amanda Burcroff, Scott Neville

For any skew-symmetric quiver, random infinite mutation sequences make c-vectors sign-coherent with probability 1.

arxiv:2605.12865 v1 · 2026-05-13 · math.CO · math.RA · math.RT

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\usepackage{pith}
\pithnumber{HNPWWAJFFRFILH7OGJXPOJCKN4}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove that with probability 1, the sequence of c-vectors obtained by random mutation of an arbitrary quiver eventually becomes sign-coherent.

C2weakest assumption

The mutation sequence must be infinite and sufficiently generic; the argument applies specifically to skew-symmetric quivers.

C3one line summary

Random mutations on skew-symmetric quivers yield sign-coherent c-vectors almost surely, proving the asymptotic sign coherence conjecture for arbitrary rank.

References

27 extracted · 27 resolved · 1 Pith anchors

[1] RealC-,G-structures and sign-coherence of cluster algebras 2025

[2] On maximal green sequences.Int 2014

[3] A conjecture onC-matrices of cluster algebras.Nagoya Math 2020

[4] Quivers with potentials and their representations II: applications to cluster algebras.J 2010

[5] Tucker J. Ervin. Unrestricted red size and sign-coherence. arXiv preprint 2401.14958, 2024 2024

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T03:09:11.475705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b5f6b01252c4a859fee326ef7244a6f206430534f9bde1137ff5df712f7aff9

Aliases

arxiv: 2605.12865 · arxiv_version: 2605.12865v1 · doi: 10.48550/arxiv.2605.12865 · pith_short_12: HNPWWAJFFRFI · pith_short_16: HNPWWAJFFRFILH7O · pith_short_8: HNPWWAJF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HNPWWAJFFRFILH7OGJXPOJCKN4 \
  | 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: 3b5f6b01252c4a859fee326ef7244a6f206430534f9bde1137ff5df712f7aff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dc30a0788e9ef2519030ddc1574989f6d92cf412323f8a4410c537cc659d00c",
    "cross_cats_sorted": [
      "math.RA",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T01:21:58Z",
    "title_canon_sha256": "2fcb5929e5504bcb1a87158d777a1a5508d08250abae8da9425610c11c611358"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12865",
    "kind": "arxiv",
    "version": 1
  }
}