Pith Number

pith:5VJGIDX5

pith:2010:5VJGIDX5V2TPEYFDBSBP7H4CAD

not attested not anchored not stored refs pending

Two ways to degenerate the Jacobian are the same

Jesse Leo Kass

arxiv:1012.2576 v3 · 2010-12-12 · math.AG · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VJGIDX5V2TPEYFDBSBP7H4CAD}

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	2026-05-18T00:39:16.347717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed52640efdaea6f260a30c82ff9f8200f55ff2e0698ac04c123e363e70d7a22d

Aliases

arxiv: 1012.2576 · arxiv_version: 1012.2576v3 · doi: 10.48550/arxiv.1012.2576 · pith_short_12: 5VJGIDX5V2TP · pith_short_16: 5VJGIDX5V2TPEYFD · pith_short_8: 5VJGIDX5

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/5VJGIDX5V2TPEYFDBSBP7H4CAD \
  | 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: ed52640efdaea6f260a30c82ff9f8200f55ff2e0698ac04c123e363e70d7a22d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a3e35c29e74858cb6e0b25d80a96796996b9f9f50e4c6887fd61bf54f5457ba",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-12-12T19:10:14Z",
    "title_canon_sha256": "81b210fa72b98009de58cb28e4d0cae0ed952f08257e530df2633967ae43f6e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2576",
    "kind": "arxiv",
    "version": 3
  }
}