Pith Number

pith:QFI3QCSR

pith:2009:QFI3QCSRS4G2SYF5TALE7ENVDV

not attested not anchored not stored refs pending

On Minimal Unsatisfiability and Time-Space Trade-offs for k-DNF Resolution

Alexander Razborov, Jakob Nordstr\"om

arxiv:0910.3127 v2 · 2009-10-16 · cs.DM · cs.CC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QFI3QCSRS4G2SYF5TALE7ENVDV}

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	2026-05-18T01:04:59.624377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8151b80a51970da960bd98164f91b51d5b1ab6baed8ffdedc2ee159949688d09

Aliases

arxiv: 0910.3127 · arxiv_version: 0910.3127v2 · doi: 10.48550/arxiv.0910.3127 · pith_short_12: QFI3QCSRS4G2 · pith_short_16: QFI3QCSRS4G2SYF5 · pith_short_8: QFI3QCSR

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/QFI3QCSRS4G2SYF5TALE7ENVDV \
  | 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: 8151b80a51970da960bd98164f91b51d5b1ab6baed8ffdedc2ee159949688d09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e32fda0e60cd52cc076b1bd5e6da7deb8cfb194d1b54a290aa2f7cb0ae37665",
    "cross_cats_sorted": [
      "cs.CC",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2009-10-16T14:33:58Z",
    "title_canon_sha256": "ace1b72a67bd92c2ffd92bd50f8272ff7ee34b9f6508b0295ed5c95f9e05e20a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.3127",
    "kind": "arxiv",
    "version": 2
  }
}