Pith Number

pith:ZGDYTR4W

pith:2026:ZGDYTR4WMUJ6HYRGFVXCHIBAXI

not attested not anchored not stored refs pending

The cosine measure of a function at a point

Chayne Planiden, Gabriel Jarry-Bolduc, Warren Hare

arxiv:2608.07716 v1 · 2026-08-07 · 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{ZGDYTR4WMUJ6HYRGFVXCHIBAXI}

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	2026-08-11T00:15:46.168454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c98789c7966513e3e2262d6e23a020ba134a55cdcccf0fea32d78ddd776ba7ec

Aliases

arxiv: 2608.07716 · arxiv_version: 2608.07716v1 · doi: 10.48550/arxiv.2608.07716 · pith_short_12: ZGDYTR4WMUJ6 · pith_short_16: ZGDYTR4WMUJ6HYRG · pith_short_8: ZGDYTR4W

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/ZGDYTR4WMUJ6HYRGFVXCHIBAXI \
  | 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: c98789c7966513e3e2262d6e23a020ba134a55cdcccf0fea32d78ddd776ba7ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9e580d7663a26c8851f869b609e96d38691440c77af3e6f75ec9150d37cb275",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-07T19:01:13Z",
    "title_canon_sha256": "ae8f269c84253c2e7a2e7962419f6da67d99a2ecd0ead5f30f5011c6d4d5ef82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07716",
    "kind": "arxiv",
    "version": 1
  }
}