Pith Number

pith:BSSIMAVB

pith:2026:BSSIMAVBNBSEV2PFQXJWWWQQGP

not attested not anchored not stored refs pending

Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture

Assar Andersson

Wheel graphs in the Kontsevich graph complex are homologous to explicit combinations of only 3- and 4-valent graphs.

arxiv:2604.11327 v2 · 2026-04-13 · math.QA · math.CO

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\usepackage{pith}
\pithnumber{BSSIMAVBNBSEV2PFQXJWWWQQGP}

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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

for every m ≥ 2, we prove that the wheel graph W_{2m+1} is homologous to an explicit linear combination of 2^{m-1} graphs, each having only 3- and 4-valent vertices.

C2weakest assumption

The explicit linear combination constructed in the paper is a cycle whose boundary equals that of the wheel graph under the standard differential of GC_d.

C3one line summary

For every m ≥ 2 the wheel graph W_{2m+1} is homologous to an explicit sum of 2^{m-1} graphs with only 3- and 4-valent vertices.

Receipt and verification

First computed	2026-05-21T01:05:18.929455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ca48602a168644ae9e585d36b5a1033f5593bb99e6a0281281c148768419860

Aliases

arxiv: 2604.11327 · arxiv_version: 2604.11327v2 · doi: 10.48550/arxiv.2604.11327 · pith_short_12: BSSIMAVBNBSE · pith_short_16: BSSIMAVBNBSEV2PF · pith_short_8: BSSIMAVB

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/BSSIMAVBNBSEV2PFQXJWWWQQGP \
  | 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: 0ca48602a168644ae9e585d36b5a1033f5593bb99e6a0281281c148768419860

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22728c84e9ea977e905ce5694eec0d1b29e4947a1ea3677a7d7606c4719816e9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-04-13T11:29:44Z",
    "title_canon_sha256": "cf321c2f33303fe3b5b1bfeac03cbb4ae71245ae5ec340b1faadc7067e16db48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11327",
    "kind": "arxiv",
    "version": 2
  }
}