Pith Number

pith:VLXKZO6G

pith:2013:VLXKZO6GDXRSTB5PZUHSSH34GY

not attested not anchored not stored refs pending

Discrete integrals based on comonotonic modularity

Jean-Luc Marichal, Miguel Couceiro

arxiv:1304.3042 v2 · 2013-04-10 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VLXKZO6GDXRSTB5PZUHSSH34GY}

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	2026-05-18T03:14:52.589455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaeeacbbc61de32987afcd0f291f7c36275328e3df4adb0d2ececedcd4eed767

Aliases

arxiv: 1304.3042 · arxiv_version: 1304.3042v2 · doi: 10.48550/arxiv.1304.3042 · pith_short_12: VLXKZO6GDXRS · pith_short_16: VLXKZO6GDXRSTB5P · pith_short_8: VLXKZO6G

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/VLXKZO6GDXRSTB5PZUHSSH34GY \
  | 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: aaeeacbbc61de32987afcd0f291f7c36275328e3df4adb0d2ececedcd4eed767

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd2a621ea47b93da35671488f91125f85d30c5837647a817ccd5b602b5209398",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-10T18:16:25Z",
    "title_canon_sha256": "4e6ddcb06ae7a77ee727ac3c8f7b5f2a7312f7f4942b8293ef5715ab2f6246dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3042",
    "kind": "arxiv",
    "version": 2
  }
}