Pith Number

pith:MCF3IV2W

pith:2000:MCF3IV2WSQ7C6I7QPJMUJ67AEA

not attested not anchored not stored refs pending

Stable maps and Quot schemes

Mihnea Popa, Mike Roth

arxiv:math/0012221 v2 · 2000-12-21 · 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{MCF3IV2WSQ7C6I7QPJMUJ67AEA}

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	2026-05-18T01:38:30.090080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

608bb45756943e2f23f07a5944fbe02019a51bc69d05fd5cf64dd52924b12570

Aliases

arxiv: math/0012221 · arxiv_version: math/0012221v2 · doi: 10.48550/arxiv.math/0012221 · pith_short_12: MCF3IV2WSQ7C · pith_short_16: MCF3IV2WSQ7C6I7Q · pith_short_8: MCF3IV2W

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/MCF3IV2WSQ7C6I7QPJMUJ67AEA \
  | 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: 608bb45756943e2f23f07a5944fbe02019a51bc69d05fd5cf64dd52924b12570

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d419fef1a5df9c82bb440e900d1cd465a7b41419bbeca66ff316ec287b313e00",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-12-21T19:18:19Z",
    "title_canon_sha256": "c493592fb8f08fc67cf119ac131a325c6ba68f0848ccf3f221da2fafea4bd32f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012221",
    "kind": "arxiv",
    "version": 2
  }
}