Pith Number

pith:US6J6GKU

pith:2016:US6J6GKUPDJ2GE52HPXVWJV6YB

not attested not anchored not stored refs pending

Unprovability of circuit upper bounds in Cook's theory PV

Igor C. Oliveira, Jan Krajicek

arxiv:1605.00263 v3 · 2016-05-01 · math.LO · 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{US6J6GKUPDJ2GE52HPXVWJV6YB}

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	2026-05-18T00:50:47.707376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4bc9f195478d3a313ba3bef5b26bec04543e981e11fc464ad26ac243fca3f56

Aliases

arxiv: 1605.00263 · arxiv_version: 1605.00263v3 · doi: 10.48550/arxiv.1605.00263 · pith_short_12: US6J6GKUPDJ2 · pith_short_16: US6J6GKUPDJ2GE52 · pith_short_8: US6J6GKU

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/US6J6GKUPDJ2GE52HPXVWJV6YB \
  | 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: a4bc9f195478d3a313ba3bef5b26bec04543e981e11fc464ad26ac243fca3f56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8ee1359375ba64161b09bad6945bf0bec3c19ebbb153a9ce97d62c92c0e20ac",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2016-05-01T15:11:04Z",
    "title_canon_sha256": "04ba4b2c1393c3f29a1988b021ecf39ead664f3554b1cf49edca2224f61f5e1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00263",
    "kind": "arxiv",
    "version": 3
  }
}