Pith Number

pith:V52JACE5

pith:2026:V52JACE5ELS74TK7KZXA64LMZM

not attested not anchored not stored refs pending

Edge-spectra supersaturation for tripartite color-critical graphs

Huiqiu Lin, Longfei Fang, Mingqing Zhai

arxiv:2608.04485 v1 · 2026-08-05 · 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{V52JACE5ELS74TK7KZXA64LMZM}

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	2026-08-06T01:35:41.821974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af7490089d22e5fe4d5f566e0f716ccb0651a0f38456aeaa41e0af06d2e704a9

Aliases

arxiv: 2608.04485 · arxiv_version: 2608.04485v1 · doi: 10.48550/arxiv.2608.04485 · pith_short_12: V52JACE5ELS7 · pith_short_16: V52JACE5ELS74TK7 · pith_short_8: V52JACE5

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/V52JACE5ELS74TK7KZXA64LMZM \
  | 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: af7490089d22e5fe4d5f566e0f716ccb0651a0f38456aeaa41e0af06d2e704a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3db77fccf52d1a0f59565ce08238b48e3e233d5d94c146a323e78fb56c978506",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-05T06:17:52Z",
    "title_canon_sha256": "bbefee7dee565e20ce1ec45e6596d97494ca414ddd498508eee08ef25c1aa9ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04485",
    "kind": "arxiv",
    "version": 1
  }
}