Pith Number

pith:XWG7ZH5F

pith:2015:XWG7ZH5FD6Y4YJJ5BCP2DGOGG7

not attested not anchored not stored refs pending

Tensors Masquerading as Matchgates: Relaxing Planarity Restrictions on Pfaffian Circuits

Jacob Turner

arxiv:1510.01541 v2 · 2015-10-06 · math.AG · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XWG7ZH5FD6Y4YJJ5BCP2DGOGG7}

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	2026-05-18T00:44:37.270561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd8dfc9fa51fb1cc253d089fa199c637e81819a6bd4da860ee8c1dbcc838dca9

Aliases

arxiv: 1510.01541 · arxiv_version: 1510.01541v2 · doi: 10.48550/arxiv.1510.01541 · pith_short_12: XWG7ZH5FD6Y4 · pith_short_16: XWG7ZH5FD6Y4YJJ5 · pith_short_8: XWG7ZH5F

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/XWG7ZH5FD6Y4YJJ5BCP2DGOGG7 \
  | 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: bd8dfc9fa51fb1cc253d089fa199c637e81819a6bd4da860ee8c1dbcc838dca9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0ea07f32ff014e00bc3bbacf844ebc15bb467706d5c503c19867990a80680fc",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-10-06T11:54:53Z",
    "title_canon_sha256": "a20aca57836fcd17f6e584f955168424db32ed8b7dc7de99775eb303bc5f5d14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01541",
    "kind": "arxiv",
    "version": 2
  }
}