Pith Number

pith:JFWKDBPP

pith:2009:JFWKDBPP5R5JH6QQOSS57REA3F

not attested not anchored not stored refs pending

Co-universal algebras associated to product systems, and gauge-invariant uniqueness theorems

Aidan Sims, Nadia S. Larsen, Sean Vittadello, Toke Meier Carlsen

arxiv:0906.4825 v2 · 2009-06-26 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JFWKDBPP5R5JH6QQOSS57REA3F}

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	2026-05-18T04:00:38.264912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

496ca185efec7a93fa1074a5dfc480d979bc4dbca5ef7727de4f399d58b0aa7b

Aliases

arxiv: 0906.4825 · arxiv_version: 0906.4825v2 · doi: 10.48550/arxiv.0906.4825 · pith_short_12: JFWKDBPP5R5J · pith_short_16: JFWKDBPP5R5JH6QQ · pith_short_8: JFWKDBPP

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/JFWKDBPP5R5JH6QQOSS57REA3F \
  | 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: 496ca185efec7a93fa1074a5dfc480d979bc4dbca5ef7727de4f399d58b0aa7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a93c363268f330e686f48620593cffa721ea711dec1104e99e4911feba1909e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-06-26T00:50:35Z",
    "title_canon_sha256": "1f3492d834f656a24218393c7557f9b32f1347279157440d5ea42f3557fda22b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.4825",
    "kind": "arxiv",
    "version": 2
  }
}