Pith Number

pith:IBK3L334

pith:2015:IBK3L334VKF6K4RKUY6S2GK6TE

not attested not anchored not stored refs pending

2-Xor revisited: satisfiability and probabilities of functions

Bernhard Gittenberger, Dani\`ele Gardy, \'Elie de Panafieu, Markus Kuba

arxiv:1511.07813 v1 · 2015-11-24 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IBK3L334VKF6K4RKUY6S2GK6TE}

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	2026-05-18T01:26:03.516070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4055b5ef7caa8be5722aa63d2d195e9922edf8df9642c22aecdffc6293f97d2f

Aliases

arxiv: 1511.07813 · arxiv_version: 1511.07813v1 · doi: 10.48550/arxiv.1511.07813 · pith_short_12: IBK3L334VKF6 · pith_short_16: IBK3L334VKF6K4RK · pith_short_8: IBK3L334

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/IBK3L334VKF6K4RKUY6S2GK6TE \
  | 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: 4055b5ef7caa8be5722aa63d2d195e9922edf8df9642c22aecdffc6293f97d2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de93ed73ad82cd93a3b952093d6f2ddcae95227950785229c195f51d6591630b",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-24T17:22:25Z",
    "title_canon_sha256": "e067442f193ad5a5d85befdb4338603e32c5945a154e93dd5d1ccb58ad37c929"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07813",
    "kind": "arxiv",
    "version": 1
  }
}