Pith Number

pith:7WFECPXT

pith:2026:7WFECPXTKSQBCNK56M2N6KWIST

not attested not anchored not stored refs pending

Counterexamples to two conjectures on modular edge colorings of graphs

Baoyindureng Wu, Chunqiang Guo

arxiv:2608.10687 v1 · 2026-08-11 · 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{7WFECPXTKSQBCNK56M2N6KWIST}

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	2026-08-12T01:23:02.670773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd8a413ef354a011355df334df2ac894e05347dff8242288262e3737c0d75e85

Aliases

arxiv: 2608.10687 · arxiv_version: 2608.10687v1 · doi: 10.48550/arxiv.2608.10687 · pith_short_12: 7WFECPXTKSQB · pith_short_16: 7WFECPXTKSQBCNK5 · pith_short_8: 7WFECPXT

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/7WFECPXTKSQBCNK56M2N6KWIST \
  | 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: fd8a413ef354a011355df334df2ac894e05347dff8242288262e3737c0d75e85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56f3dad9259b64497d1229dc4752980adbc909d6d1cf5472e80b7631ef9a64c7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-11T09:11:34Z",
    "title_canon_sha256": "83c35389536d3c64c4a3dc8ad16cb0587739f621b3c4cc7e4be5851d6260d172"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.10687",
    "kind": "arxiv",
    "version": 1
  }
}