Pith Number

pith:E4XZUMV4

pith:2007:E4XZUMV4UCI66N7CWNEDXWMSAP

not attested not anchored not stored refs pending

Orbit closures of directing modules are regular in codimension one

Grzegorz Bobinski

arxiv:0712.1246 v1 · 2007-12-07 · math.RT · 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{E4XZUMV4UCI66N7CWNEDXWMSAP}

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	2026-05-18T02:58:11.970634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

272f9a32bca091ef37e2b3483bd99203c345a3796b8fded29b9269cec9c9091c

Aliases

arxiv: 0712.1246 · arxiv_version: 0712.1246v1 · doi: 10.48550/arxiv.0712.1246 · pith_short_12: E4XZUMV4UCI6 · pith_short_16: E4XZUMV4UCI66N7C · pith_short_8: E4XZUMV4

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/E4XZUMV4UCI66N7CWNEDXWMSAP \
  | 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: 272f9a32bca091ef37e2b3483bd99203c345a3796b8fded29b9269cec9c9091c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d514ae6b66c8f13e7958d16746e417831ac771a819580a61e1ecfae17c34038",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.RT",
    "submitted_at": "2007-12-07T23:15:03Z",
    "title_canon_sha256": "b6c0abe89a6e1c99df23bce263194d443ad51ff6785ec7a7e147e302c0f72f86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1246",
    "kind": "arxiv",
    "version": 1
  }
}