Pith Number

pith:XU7AH4BI

pith:2026:XU7AH4BI3V7SDZJFSOPHR6Z76Y

not attested not anchored not stored refs pending

Chromatic symmetric functions of claw-free graphs are not Schur positive

Alejandro H. Morales, Jacob P. Matherne

arxiv:2607.21508 v1 · 2026-07-23 · 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{XU7AH4BI3V7SDZJFSOPHR6Z76Y}

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	2026-07-24T01:24:36.851682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd3e03f028dd7f21e525939e78fb3ff600d6cb08808a24eeda543e88a43fe2c2

Aliases

arxiv: 2607.21508 · arxiv_version: 2607.21508v1 · doi: 10.48550/arxiv.2607.21508 · pith_short_12: XU7AH4BI3V7S · pith_short_16: XU7AH4BI3V7SDZJF · pith_short_8: XU7AH4BI

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/XU7AH4BI3V7SDZJFSOPHR6Z76Y \
  | 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: bd3e03f028dd7f21e525939e78fb3ff600d6cb08808a24eeda543e88a43fe2c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "469343b066b21df392edbb1100d584d91d55e0d1776f21444f62db538e8c594a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-23T16:54:51Z",
    "title_canon_sha256": "7f1f66141a8df551e8bedaa00ee82cd924631246cdc65d2a1051432d4c4dc9d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21508",
    "kind": "arxiv",
    "version": 1
  }
}