Pith Number

pith:J4WXUXCH

pith:2026:J4WXUXCHWX66KMNU4Q3RRQ2PHM

not attested not anchored not stored refs pending

Ideal G{\aa}rding polynomials

Biao Ma, Hao Fang

arxiv:2607.16832 v1 · 2026-07-18 · math.CO · math.AP · math.CA · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J4WXUXCHWX66KMNU4Q3RRQ2PHM}

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	2026-07-21T01:21:01.197173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f2d7a5c47b5fde531b4e43718c34f3b0b3cfeb60abd00bfba5950ab4fca0468

Aliases

arxiv: 2607.16832 · arxiv_version: 2607.16832v1 · doi: 10.48550/arxiv.2607.16832 · pith_short_12: J4WXUXCHWX66 · pith_short_16: J4WXUXCHWX66KMNU · pith_short_8: J4WXUXCH

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/J4WXUXCHWX66KMNU4Q3RRQ2PHM \
  | 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: 4f2d7a5c47b5fde531b4e43718c34f3b0b3cfeb60abd00bfba5950ab4fca0468

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "389597f9127e095268650f99b3279e8bbea00a227d0ceb6ccc646bf181bfcb64",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA",
      "math.OC",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-18T14:07:17Z",
    "title_canon_sha256": "d631f8ea29b12e14411fbe4bf5fdb323df1dce0eb36ac1d303f3ed136efe9d20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16832",
    "kind": "arxiv",
    "version": 1
  }
}