Pith Number

pith:7VOWP34U

pith:2016:7VOWP34UAKE5MW7JUV4FOQDIJD

not attested not anchored not stored refs pending

Fa\`a di Bruno for operads and internal algebras

Joachim Kock, Mark Weber

arxiv:1609.03276 v1 · 2016-09-12 · math.CT · math.AT · 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{7VOWP34UAKE5MW7JUV4FOQDIJD}

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	2026-05-17T23:41:31.537821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd5d67ef940289d65be9a57857406848f9b3f7a03feea17a8c76371a57678c5a

Aliases

arxiv: 1609.03276 · arxiv_version: 1609.03276v1 · doi: 10.48550/arxiv.1609.03276 · pith_short_12: 7VOWP34UAKE5 · pith_short_16: 7VOWP34UAKE5MW7J · pith_short_8: 7VOWP34U

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/7VOWP34UAKE5MW7JUV4FOQDIJD \
  | 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: fd5d67ef940289d65be9a57857406848f9b3f7a03feea17a8c76371a57678c5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9459972c3a2963db13fbb1c48397638f9aef49bf2f82c8dc7eb5dacb2648075",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2016-09-12T05:55:49Z",
    "title_canon_sha256": "874397eefa76c56256af2135958462bcaea84d7c13fd3eddb0056d8f757e830b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03276",
    "kind": "arxiv",
    "version": 1
  }
}