Pith Number

pith:UMARYFTL

pith:2011:UMARYFTLPSOEQORBVW5MFURX7K

not attested not anchored not stored refs pending

Reduction maps and minimal model theory

Brian Lehmann, Yoshinori Gongyo

arxiv:1103.1605 v2 · 2011-03-08 · 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{UMARYFTLPSOEQORBVW5MFURX7K}

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	2026-05-17T23:53:36.693160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3011c166b7c9c483a21adbac2d237fabde676ac348f767999fb413648bf0285

Aliases

arxiv: 1103.1605 · arxiv_version: 1103.1605v2 · doi: 10.48550/arxiv.1103.1605 · pith_short_12: UMARYFTLPSOE · pith_short_16: UMARYFTLPSOEQORB · pith_short_8: UMARYFTL

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/UMARYFTLPSOEQORBVW5MFURX7K \
  | 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: a3011c166b7c9c483a21adbac2d237fabde676ac348f767999fb413648bf0285

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d420fffea47256f60a270aeaf0a2c8915f2ff29073d7957c8f60d9e7e0707b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-03-08T19:05:08Z",
    "title_canon_sha256": "9a72804a65f54756b3d30b3a7d3aa604c3057af807cf4f37381fb526b6f7cdee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1605",
    "kind": "arxiv",
    "version": 2
  }
}