Pith Number

pith:2M4CVGFV

pith:2007:2M4CVGFVNTZHXRLONHLIMMU5WJ

not attested not anchored not stored refs pending

A canonical bundle formular of projective Lagrangian fibrations

Daisuke Matsushita

arxiv:0710.0122 v2 · 2007-09-30 · 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{2M4CVGFVNTZHXRLONHLIMMU5WJ}

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	2026-05-18T00:56:47.221476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3382a98b56cf27bc56e69d686329db27da05c234e7ade760ac16e7c3f1dafba

Aliases

arxiv: 0710.0122 · arxiv_version: 0710.0122v2 · doi: 10.48550/arxiv.0710.0122 · pith_short_12: 2M4CVGFVNTZH · pith_short_16: 2M4CVGFVNTZHXRLO · pith_short_8: 2M4CVGFV

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/2M4CVGFVNTZHXRLONHLIMMU5WJ \
  | 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: d3382a98b56cf27bc56e69d686329db27da05c234e7ade760ac16e7c3f1dafba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "885ae8969c9afce6d762cc07f8b1ed7f572110ca7e8cc20a1f813710e74e6524",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-09-30T10:05:04Z",
    "title_canon_sha256": "10621f038ed7f6d2ff7ff584573d22421e94a22185ceaa3127279611cd8e8a59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.0122",
    "kind": "arxiv",
    "version": 2
  }
}