Pith Number

pith:4W35QQOL

pith:2012:4W35QQOLHI6DDAPKZUTNQEW7WY

not attested not anchored not stored refs pending

Legendre-type integrands and convex integral functions

Jonathan M. Borwein, Liangjin Yao

arxiv:1208.5217 v1 · 2012-08-26 · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4W35QQOLHI6DDAPKZUTNQEW7WY}

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	2026-05-18T03:47:00.121863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5b7d841cb3a3c3181eacd26d812dfb636acf7b812bf99ab0f5cd1b7b21b05fd

Aliases

arxiv: 1208.5217 · arxiv_version: 1208.5217v1 · doi: 10.48550/arxiv.1208.5217 · pith_short_12: 4W35QQOLHI6D · pith_short_16: 4W35QQOLHI6DDAPK · pith_short_8: 4W35QQOL

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/4W35QQOLHI6DDAPKZUTNQEW7WY \
  | 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: e5b7d841cb3a3c3181eacd26d812dfb636acf7b812bf99ab0f5cd1b7b21b05fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2c70e323323bed4eabfb676e2c75eea0b5fa74379b211c8a0583b5446f535c4",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-26T11:56:33Z",
    "title_canon_sha256": "fcab98300cb57942b100eaa03849e7f53c183f6371d4e2b6980a2ab8338cde74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5217",
    "kind": "arxiv",
    "version": 1
  }
}