Pith Number

pith:3VPIVWQF

pith:2015:3VPIVWQFIBLDBXVSFZFGE3DD2F

not attested not anchored not stored refs pending

Exact bounds of the M{\"o}bius inverse of monotone set functions

CES), Michel Grabisch (EEP-PSE, Pedro Miranda

arxiv:1503.08550 v1 · 2015-03-30 · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VPIVWQFIBLDBXVSFZFGE3DD2F}

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	2026-05-18T02:20:01.441343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd5e8ada05405630deb22e4a626c63d1612f5a08f6d91fb8317e09f9b2529234

Aliases

arxiv: 1503.08550 · arxiv_version: 1503.08550v1 · doi: 10.48550/arxiv.1503.08550 · pith_short_12: 3VPIVWQFIBLD · pith_short_16: 3VPIVWQFIBLDBXVS · pith_short_8: 3VPIVWQF

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/3VPIVWQFIBLDBXVSFZFGE3DD2F \
  | 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: dd5e8ada05405630deb22e4a626c63d1612f5a08f6d91fb8317e09f9b2529234

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89a54656578c8efcb24a224d34142aca7e0f9cd4fce2379e3d4ca3b6c8638047",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-03-30T06:29:40Z",
    "title_canon_sha256": "e46f1a0ced596597c298b3462064667733b63c2f39ab0192af58243059037e65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08550",
    "kind": "arxiv",
    "version": 1
  }
}