Pith Number

pith:AFP4YV2A

pith:2015:AFP4YV2APAY7USM6FUIW75J4PT

not attested not anchored not stored refs pending

The wonderland of reflections

Jakub Opr\v{s}al, Libor Barto, Michael Pinsker

arxiv:1510.04521 v2 · 2015-10-15 · math.LO · cs.CC · cs.LO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AFP4YV2APAY7USM6FUIW75J4PT}

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	2026-05-18T00:52:17.679109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

015fcc57407831fa499e2d116ff53c7cff47383392b9c6a4a66da61c21cc5122

Aliases

arxiv: 1510.04521 · arxiv_version: 1510.04521v2 · doi: 10.48550/arxiv.1510.04521 · pith_short_12: AFP4YV2APAY7 · pith_short_16: AFP4YV2APAY7USM6 · pith_short_8: AFP4YV2A

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/AFP4YV2APAY7USM6FUIW75J4PT \
  | 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: 015fcc57407831fa499e2d116ff53c7cff47383392b9c6a4a66da61c21cc5122

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b1d118b974bf5c9a6c150119a0b760644865a0f1ef3f9df17adc9ff23d2dc48",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.LO",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2015-10-15T13:13:13Z",
    "title_canon_sha256": "1757af101ce415344750bd965e9a3f1daaf514b614daf172ceb0c0aebd94da89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04521",
    "kind": "arxiv",
    "version": 2
  }
}