Pith Number

pith:5H2RKQXR

pith:2021:5H2RKQXRLT5MXKXSZ6IDQMOKUJ

not attested not anchored not stored refs pending

Combinatorics of NC-Probability Spaces with Independent Constants

Carlos Dias-Aguilera, Carlos Vargas, Jorge Santos, Tulio Gaxiola

arxiv:2109.06019 v1 · 2021-09-13 · math.PR · 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{5H2RKQXRLT5MXKXSZ6IDQMOKUJ}

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	2026-07-05T03:13:44.729877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9f51542f15cfacbaaf2cf903831caa2458985dcd8594eda30e38a6438b9fefe

Aliases

arxiv: 2109.06019 · arxiv_version: 2109.06019v1 · doi: 10.48550/arxiv.2109.06019 · pith_short_12: 5H2RKQXRLT5M · pith_short_16: 5H2RKQXRLT5MXKXS · pith_short_8: 5H2RKQXR

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/5H2RKQXRLT5MXKXSZ6IDQMOKUJ \
  | 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: e9f51542f15cfacbaaf2cf903831caa2458985dcd8594eda30e38a6438b9fefe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e015f86744a9bd43e674fede179980d7a8ea9b69d57e998c982da7b0d849aa71",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-09-13T14:51:46Z",
    "title_canon_sha256": "3a8b3b37e153a3a77349d7ab50c4df2dd87589d2577cc56056cc47fc9b3f76fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.06019",
    "kind": "arxiv",
    "version": 1
  }
}