Pith Number

pith:OPDZUY7C

pith:2016:OPDZUY7CIY342XZDFQOSRUXRVV

not attested not anchored not stored refs pending

Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane -- Vaquie

Julie Decaup, Mark Spivakovsky, Wael Mahboub

arxiv:1611.06392 v1 · 2016-11-19 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OPDZUY7CIY342XZDFQOSRUXRVV}

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	2026-05-18T00:57:36.885532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73c79a63e24637cd5f232c1d28d2f1ad589a8327a8f1e9458277d4307285fc11

Aliases

arxiv: 1611.06392 · arxiv_version: 1611.06392v1 · doi: 10.48550/arxiv.1611.06392 · pith_short_12: OPDZUY7CIY34 · pith_short_16: OPDZUY7CIY342XZD · pith_short_8: OPDZUY7C

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/OPDZUY7CIY342XZDFQOSRUXRVV \
  | 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: 73c79a63e24637cd5f232c1d28d2f1ad589a8327a8f1e9458277d4307285fc11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c646bb96a732ffba2ffe24e5dede91d31f518b96671f28ac5a69656ee607acc",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-11-19T16:07:49Z",
    "title_canon_sha256": "80653213681511a3ae03ef881ff10b6e31b4e62ca7d1c2f34ac75930fe10b4c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06392",
    "kind": "arxiv",
    "version": 1
  }
}