Pith Number

pith:KEW7ZC2L

pith:2009:KEW7ZC2LS63RTCZ25Y2UHFCLF3

not attested not anchored not stored refs pending

On the circuit-size of inverses

Jean-Camille Birget

arxiv:0912.3730 v2 · 2009-12-18 · 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{KEW7ZC2LS63RTCZ25Y2UHFCLF3}

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	2026-05-18T04:27:58.248957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

512dfc8b4b97b7198b3aee3543944b2ee19679d34439f2218269a5cadc6640ce

Aliases

arxiv: 0912.3730 · arxiv_version: 0912.3730v2 · doi: 10.48550/arxiv.0912.3730 · pith_short_12: KEW7ZC2LS63R · pith_short_16: KEW7ZC2LS63RTCZ2 · pith_short_8: KEW7ZC2L

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/KEW7ZC2LS63RTCZ25Y2UHFCLF3 \
  | 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: 512dfc8b4b97b7198b3aee3543944b2ee19679d34439f2218269a5cadc6640ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b09a6cb8065c08cc2f75135f742808240b2904a7145485596aa6211f06ff2f9e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2009-12-18T16:34:15Z",
    "title_canon_sha256": "8889965a698822809d17e719a9b500c4cdb91c8ca0f8fb372db163db2faded40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3730",
    "kind": "arxiv",
    "version": 2
  }
}