Pith Number

pith:WY35XULJ

pith:2010:WY35XULJCLTNF3BAC4UIOHGRRR

not attested not anchored not stored refs pending

Symmetric Determinantal Representation of Formulas and Weakly Skew Circuits

Bruno Grenet (LIP), Erich Kaltofen, Natacha Portier (LIP), Pascal Koiran (LIP)

arxiv:1007.3804 v4 · 2010-07-22 · cs.CC · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WY35XULJCLTNF3BAC4UIOHGRRR}

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	2026-05-18T03:42:34.155221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b637dbd16912e6d2ec201728871cd18c4e43aa7ee4016349d469095cd521e829

Aliases

arxiv: 1007.3804 · arxiv_version: 1007.3804v4 · doi: 10.48550/arxiv.1007.3804 · pith_short_12: WY35XULJCLTN · pith_short_16: WY35XULJCLTNF3BA · pith_short_8: WY35XULJ

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/WY35XULJCLTNF3BAC4UIOHGRRR \
  | 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: b637dbd16912e6d2ec201728871cd18c4e43aa7ee4016349d469095cd521e829

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6699dbc1e33a51f31c5a6c59b500976df0de6223e3fd7426cb54862d15672bf",
    "cross_cats_sorted": [
      "cs.SC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2010-07-22T06:07:33Z",
    "title_canon_sha256": "451cf9a1bdc66b8f9080446a0fe06b2795f272fb1c1676bf0fcee5aa96797bd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3804",
    "kind": "arxiv",
    "version": 4
  }
}