Pith Number

pith:GANPRG4F

pith:2006:GANPRG4FK5QW2LWWX4URZG4KQL

not attested not anchored not stored refs pending

Geometric collections and Castelnuovo-Mumford Regularity

L. Costa, R.M. Mir\'o-Roig

arxiv:math/0609561 v1 · 2006-09-20 · 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{GANPRG4FK5QW2LWWX4URZG4KQL}

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	2026-05-17T23:47:21.388695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

301af89b8557616d2ed6bf291c9b8a82d54060443346999408bcc16ee179bc4a

Aliases

arxiv: math/0609561 · arxiv_version: math/0609561v1 · doi: 10.48550/arxiv.math/0609561 · pith_short_12: GANPRG4FK5QW · pith_short_16: GANPRG4FK5QW2LWW · pith_short_8: GANPRG4F

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/GANPRG4FK5QW2LWWX4URZG4KQL \
  | 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: 301af89b8557616d2ed6bf291c9b8a82d54060443346999408bcc16ee179bc4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f07634b34dacd2db4add2ec8cc0da8c8373f0efe75195436d5b0e94f8d3dabe",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-09-20T14:05:17Z",
    "title_canon_sha256": "041b593ced7574d1756d0b708370f6c17499e36a2a7516537a05a433a6d8fea2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609561",
    "kind": "arxiv",
    "version": 1
  }
}