Pith Number

pith:X7RL5G6E

pith:2007:X7RL5G6EWTBXHITRSCTNSEV3BM

not attested not anchored not stored refs pending

On existence of log minimal models

Caucher Birkar

arxiv:0706.1792 v3 · 2007-06-12 · 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{X7RL5G6EWTBXHITRSCTNSEV3BM}

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	2026-05-17T23:53:20.265644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfe2be9bc4b4c373a27190a6d912bb0b3fe062f18850ff411db1e8408f05ac00

Aliases

arxiv: 0706.1792 · arxiv_version: 0706.1792v3 · doi: 10.48550/arxiv.0706.1792 · pith_short_12: X7RL5G6EWTBX · pith_short_16: X7RL5G6EWTBXHITR · pith_short_8: X7RL5G6E

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/X7RL5G6EWTBXHITRSCTNSEV3BM \
  | 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: bfe2be9bc4b4c373a27190a6d912bb0b3fe062f18850ff411db1e8408f05ac00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "017ae4a4771d6cee5811e0aeef2e2281bef2db56b51f5c65d5da947358217f88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-06-12T21:36:47Z",
    "title_canon_sha256": "a004c0db845c8dffb41c26aad5986deb39bea8bea582d4330a0e1c756af3e42d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.1792",
    "kind": "arxiv",
    "version": 3
  }
}