Pith Number

pith:HCGUQ4IJ

pith:2007:HCGUQ4IJVY33BGMN6QSWNBR2AW

not attested not anchored not stored refs pending

On Weighted Residual and Past Entropies

Antonio Di Crescenzo, Maria Longobardi

arxiv:math/0703489 v3 · 2007-03-16 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HCGUQ4IJVY33BGMN6QSWNBR2AW}

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	2026-05-18T04:19:22.502566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

388d487109ae37b0998df42566863a05bc949d919d48bf2ae1c168c66f28f45e

Aliases

arxiv: math/0703489 · arxiv_version: math/0703489v3 · doi: 10.48550/arxiv.math/0703489 · pith_short_12: HCGUQ4IJVY33 · pith_short_16: HCGUQ4IJVY33BGMN · pith_short_8: HCGUQ4IJ

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/HCGUQ4IJVY33BGMN6QSWNBR2AW \
  | 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: 388d487109ae37b0998df42566863a05bc949d919d48bf2ae1c168c66f28f45e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10724bafdba3a4d52b3c1e86f188f0606eefd3c6267c901ee616872ce124da3f",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2007-03-16T13:42:39Z",
    "title_canon_sha256": "932b765b7001f5ee5b9ae2444f2d31e273b434fcdbff817115bf739daada6a63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703489",
    "kind": "arxiv",
    "version": 3
  }
}