Pith Number

pith:HILEXR4F

pith:2024:HILEXR4FHLQMZ43WM6MV6L5DXJ

not attested not anchored not stored refs pending

Rational homotopy theory of operad modules through colored operads

Thomas Willwacher

arxiv:2412.11182 v1 · 2024-12-15 · math.AT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HILEXR4FHLQMZ43WM6MV6L5DXJ}

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	2026-07-05T09:49:28.592614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a164bc7853ae0ccf37667995f2fa3ba7e1562488ada33b6c1e9f94f35d87264

Aliases

arxiv: 2412.11182 · arxiv_version: 2412.11182v1 · doi: 10.48550/arxiv.2412.11182 · pith_short_12: HILEXR4FHLQM · pith_short_16: HILEXR4FHLQMZ43W · pith_short_8: HILEXR4F

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/HILEXR4FHLQMZ43WM6MV6L5DXJ \
  | 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: 3a164bc7853ae0ccf37667995f2fa3ba7e1562488ada33b6c1e9f94f35d87264

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7911550c6efa959a00523b7ffb94543b43683d61c1242d9075e1fbd6917f1331",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2024-12-15T13:24:05Z",
    "title_canon_sha256": "a0a81b555abcbe9bd57a009edc1b3ab2099bbeb4a3998a602ec2a72631524597"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11182",
    "kind": "arxiv",
    "version": 1
  }
}