Pith Number

pith:YOKD6STM

pith:2026:YOKD6STMOUJF3KLWL63KQ5TRT7

not attested not anchored not stored refs pending

Quasimonophobic graphs and degree spectral sequences in discrete cubical homology

Mark Behrens, Samira Sahar Jamil

Quasimonophobicity on graphs forces the degree spectral sequence of discrete cubical homology to vanish in selected bidegrees and identifies injective homology with the homology of the filled CW complex, enabling explicit computation of H_2 on Greene sphere graphs.

arxiv:2605.03894 v2 · 2026-05-05 · math.AT · math.CO

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\usepackage{pith}
\pithnumber{YOKD6STMOUJF3KLWL63KQ5TRT7}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

Quasimonophobicity implies both the vanishing of the degree spectral sequence in certain bidegrees and that H_n^{inj}(G) is isomorphic to the homology of the CW complex obtained by filling in subcubes of the graph; these results are applied to compute H_2(G_n^{sph}).

C2weakest assumption

That the combinatorial condition of quasimonophobicity, once imposed, is sufficient to guarantee both the spectral-sequence vanishing and the CW-complex isomorphism without additional hidden restrictions on the graphs or on the choice of singular cubes.

C3one line summary

Receipt and verification

First computed	2026-06-08T01:04:06.483738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3943f4a6c75125da9765fb6a876719fd064f2db1db763d7fb885dc9e8f38163

Aliases

arxiv: 2605.03894 · arxiv_version: 2605.03894v2 · doi: 10.48550/arxiv.2605.03894 · pith_short_12: YOKD6STMOUJF · pith_short_16: YOKD6STMOUJF3KLW · pith_short_8: YOKD6STM

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/YOKD6STMOUJF3KLWL63KQ5TRT7 \
  | 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: c3943f4a6c75125da9765fb6a876719fd064f2db1db763d7fb885dc9e8f38163

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "402174088ee280000f743316125f6ca70ed7cf0efa08bca54d211dc06c3eb03a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-05-05T15:50:09Z",
    "title_canon_sha256": "a7cafbdc5df1eeb81fce698a8b808027038c18f8906c97a47a03d992aecbd55b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03894",
    "kind": "arxiv",
    "version": 2
  }
}