Pith Number

pith:VQJ3GQXU

pith:2013:VQJ3GQXUDYGGV46YP4RRIT5BEP

not attested not anchored not stored refs pending

Divergence for s-concave and log concave functions

Elisabeth M. Werner, Umut Caglar

arxiv:1307.5409 v1 · 2013-07-20 · 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{VQJ3GQXUDYGGV46YP4RRIT5BEP}

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	2026-05-18T03:17:55.876346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac13b342f41e0c6af3d87f23144fa123e6f39ebb13a5bbbecb10a8821fffd46e

Aliases

arxiv: 1307.5409 · arxiv_version: 1307.5409v1 · doi: 10.48550/arxiv.1307.5409 · pith_short_12: VQJ3GQXUDYGG · pith_short_16: VQJ3GQXUDYGGV46Y · pith_short_8: VQJ3GQXU

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/VQJ3GQXUDYGGV46YP4RRIT5BEP \
  | 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: ac13b342f41e0c6af3d87f23144fa123e6f39ebb13a5bbbecb10a8821fffd46e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "946e86519fb059c896033efd31ba6ff8e448b034934cc40777d82382683dc940",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-20T11:08:15Z",
    "title_canon_sha256": "2497592e15a0b87fcd9a107b943d49b6aff56663197c758b28a8a6d6fb6deae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5409",
    "kind": "arxiv",
    "version": 1
  }
}