Pith Number

pith:XMGV4O7Z

pith:2018:XMGV4O7ZM46JIGLJII7S2WPQUT

not attested not anchored not stored refs pending

Upper and lower bounds for the Bregman divergence

Benjamin Sprung

arxiv:1808.00772 v1 · 2018-08-02 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XMGV4O7ZM46JIGLJII7S2WPQUT}

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	2026-05-17T23:55:55.812253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3

Aliases

arxiv: 1808.00772 · arxiv_version: 1808.00772v1 · doi: 10.48550/arxiv.1808.00772 · pith_short_12: XMGV4O7ZM46J · pith_short_16: XMGV4O7ZM46JIGLJ · pith_short_8: XMGV4O7Z

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/XMGV4O7ZM46JIGLJII7S2WPQUT \
  | 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: bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef8b0577bafef850f87e810282f3d51531dead436da1a241c29a30087aa7c4a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2018-08-02T12:03:04Z",
    "title_canon_sha256": "e993a43b9eeb0e502802cd0fa1250ff71ccf4eeb3b9834ec4decfcfba499c6b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.00772",
    "kind": "arxiv",
    "version": 1
  }
}