Pith Number

pith:4Q5EYYQW

pith:2025:4Q5EYYQWVYPXCVEW6BS6XDDTVO

not attested not anchored not stored refs pending

Maximum Likelihood, permutohedra and Associativity Equations

No\'emie C. Combe

arxiv:2501.01345 v1 · 2025-01-02 · math.AG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4Q5EYYQWVYPXCVEW6BS6XDDTVO}

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	2026-07-05T09:56:18.435304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e43a4c6216ae1f715496f065eb8c73abbfde702d27384c92ab4c9767fb4dfabe

Aliases

arxiv: 2501.01345 · arxiv_version: 2501.01345v1 · doi: 10.48550/arxiv.2501.01345 · pith_short_12: 4Q5EYYQWVYPX · pith_short_16: 4Q5EYYQWVYPXCVEW · pith_short_8: 4Q5EYYQW

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/4Q5EYYQWVYPXCVEW6BS6XDDTVO \
  | 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: e43a4c6216ae1f715496f065eb8c73abbfde702d27384c92ab4c9767fb4dfabe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2153450624aec5db91490547fcd98eca472e3abf5f788fb307e31a6150f63cb4",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-01-02T16:53:35Z",
    "title_canon_sha256": "5dea77a7c5776590b8ad6d9feee5a36a45ff89659cbfc6131376c3506b44fd9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.01345",
    "kind": "arxiv",
    "version": 1
  }
}