Pith Number

pith:3RD32UAQ

pith:2026:3RD32UAQBJXH3IE5ANCLDBZBTD

not attested not anchored not stored refs pending

Exact Homomorphism Thresholds Beyond Cliques

Chong Shangguan, Mingyuan Rong, Xinqi Huang

arxiv:2607.28241 v1 · 2026-07-30 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3RD32UAQBJXH3IE5ANCLDBZBTD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-07-31T01:36:53.819320Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

dc47bd50100a6e7da09d0344b1872198f54066b76f6e92655ae37507f4b08ea7

Aliases

arxiv: 2607.28241 · arxiv_version: 2607.28241v1 · doi: 10.48550/arxiv.2607.28241 · pith_short_12: 3RD32UAQBJXH · pith_short_16: 3RD32UAQBJXH3IE5 · pith_short_8: 3RD32UAQ

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/3RD32UAQBJXH3IE5ANCLDBZBTD \
  | 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: dc47bd50100a6e7da09d0344b1872198f54066b76f6e92655ae37507f4b08ea7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82c56a02f875c0bfcf83f63c045b02f970a9484f507c8c19e768ad69397c7feb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-30T14:06:22Z",
    "title_canon_sha256": "d15a0dcd5aad3969a14d18d0ff3454171de3d1b07daeea80bb2a13afeefe2b7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28241",
    "kind": "arxiv",
    "version": 1
  }
}