Pith Number

pith:AMBMED4Q

pith:2015:AMBMED4QZBRL75I63VDMXXRST6

not attested not anchored not stored refs pending

Concavity of some entropies

Ioan Rasa

arxiv:1512.02364 v1 · 2015-12-08 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AMBMED4QZBRL75I63VDMXXRST6}

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	2026-05-18T01:24:44.827068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0302c20f90c862bff51edd46cbde329f8a0bcc738ea5f39c7c10f650c966b315

Aliases

arxiv: 1512.02364 · arxiv_version: 1512.02364v1 · doi: 10.48550/arxiv.1512.02364 · pith_short_12: AMBMED4QZBRL · pith_short_16: AMBMED4QZBRL75I6 · pith_short_8: AMBMED4Q

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/AMBMED4QZBRL75I63VDMXXRST6 \
  | 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: 0302c20f90c862bff51edd46cbde329f8a0bcc738ea5f39c7c10f650c966b315

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "129e53c12930f818220085fa0e5a7cc5aba8b6ef0035975c791749f2250e602e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-08T08:30:29Z",
    "title_canon_sha256": "d46bea3d5faffbc185afed7552bc2d1f0b5a1b848cfd1c1adfae5b54198228a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02364",
    "kind": "arxiv",
    "version": 1
  }
}