Pith Number

pith:CAC5SMYU

pith:2015:CAC5SMYUJEGF7HWAYVTI57DU3S

not attested not anchored not stored refs pending

A short proof of the zero-two law for cosine functions

Jean Esterle (IMB)

arxiv:1505.06065 v1 · 2015-05-22 · 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{CAC5SMYUJEGF7HWAYVTI57DU3S}

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	2026-05-18T02:03:49.239870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1005d93314490c5f9ec0c5668efc74dc9ca55807d8e3c90b2382e9f288bca16a

Aliases

arxiv: 1505.06065 · arxiv_version: 1505.06065v1 · doi: 10.48550/arxiv.1505.06065 · pith_short_12: CAC5SMYUJEGF · pith_short_16: CAC5SMYUJEGF7HWA · pith_short_8: CAC5SMYU

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/CAC5SMYUJEGF7HWAYVTI57DU3S \
  | 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: 1005d93314490c5f9ec0c5668efc74dc9ca55807d8e3c90b2382e9f288bca16a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac87d8dae4ff65442b9672aa306161ad3ad727bf3ab23153375192b62bc415e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-05-22T13:25:55Z",
    "title_canon_sha256": "dd133e88db24afb6de0024c7bcb51b23fdad295a2ce7cc9db2dcda1b32eaa83c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06065",
    "kind": "arxiv",
    "version": 1
  }
}