Pith Number

pith:3ELG2ZKI

pith:2007:3ELG2ZKICGK3TDM3WGZOW5VHTI

not attested not anchored not stored refs pending

Automatically reduced degenerations of automatically normal varieties

Allen Knutson

arxiv:0709.3999 v1 · 2007-09-25 · 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{3ELG2ZKICGK3TDM3WGZOW5VHTI}

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.

Cited by

1 paper in Pith

The Moduli Space of Twisted Exact Differential Forms on Curves in Positive Characteristic

Receipt and verification

First computed	2026-07-04T15:04:29.526786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9166d65481195b98d9bb1b2eb76a79a1214f4fcbbc3fa4074d10f0004f91e30

Aliases

arxiv: 0709.3999 · arxiv_version: 0709.3999v1 · doi: 10.48550/arxiv.0709.3999 · pith_short_12: 3ELG2ZKICGK3 · pith_short_16: 3ELG2ZKICGK3TDM3 · pith_short_8: 3ELG2ZKI

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/3ELG2ZKICGK3TDM3WGZOW5VHTI \
  | 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: d9166d65481195b98d9bb1b2eb76a79a1214f4fcbbc3fa4074d10f0004f91e30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a51b88aeaa52d4be40029a1dcb04b6bf6e0d485996d57dec12f80b295212dbea",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-09-25T18:16:45Z",
    "title_canon_sha256": "ebb95a866ba36aa725b5331d8e45b6eceab419687ed8c7f29b7881558de5dc90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.3999",
    "kind": "arxiv",
    "version": 1
  }
}