Pith Number

pith:COJZCIZF

pith:2025:COJZCIZFMFFKEEQDZANAD5DVKL

not attested not anchored not stored refs pending

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism

Jakob Ulmer

arxiv:2507.15445 v1 · 2025-07-21 · math.QA · math-ph · math.AT · math.MP · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{COJZCIZFMFFKEEQDZANAD5DVKL}

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	2026-07-05T11:40:57.965133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1393912325614aa21203c81a01f47552f1382d7e07051a08f466fc0e17835821

Aliases

arxiv: 2507.15445 · arxiv_version: 2507.15445v1 · doi: 10.48550/arxiv.2507.15445 · pith_short_12: COJZCIZFMFFK · pith_short_16: COJZCIZFMFFKEEQD · pith_short_8: COJZCIZF

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/COJZCIZFMFFKEEQDZANAD5DVKL \
  | 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: 1393912325614aa21203c81a01f47552f1382d7e07051a08f466fc0e17835821

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f5f22d380acf89f06c1acab7753e81d42e3523a9468399ca62145a18604f15c",
    "cross_cats_sorted": [
      "math-ph",
      "math.AT",
      "math.MP",
      "math.SG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2025-07-21T09:53:52Z",
    "title_canon_sha256": "628736b9403a8901cacd3a03323f76340bd01736d969d97dd9ae4e193fb65848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15445",
    "kind": "arxiv",
    "version": 1
  }
}