Pith Number

pith:CK557HBX

pith:2012:CK557HBX45I3WMWO5MKNB2GHPB

not attested not anchored not stored refs pending

Estimates for the norms of products of sines and cosines

Jordan Bell

arxiv:1210.7380 v1 · 2012-10-27 · math.CA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CK557HBX45I3WMWO5MKNB2GHPB}

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	2026-05-18T03:42:10.241158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12bbdf9c37e751bb32ceeb14d0e8c7784fd61ed721c03b69366fb5aca0894991

Aliases

arxiv: 1210.7380 · arxiv_version: 1210.7380v1 · doi: 10.48550/arxiv.1210.7380 · pith_short_12: CK557HBX45I3 · pith_short_16: CK557HBX45I3WMWO · pith_short_8: CK557HBX

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/CK557HBX45I3WMWO5MKNB2GHPB \
  | 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: 12bbdf9c37e751bb32ceeb14d0e8c7784fd61ed721c03b69366fb5aca0894991

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf683513f80b196062d69e91c313a1c9cf0719434e6a07458bdc9406a892fb9b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-10-27T22:47:53Z",
    "title_canon_sha256": "4f28c32cf8a0b15e848277c5dbaa520dcf7d17a15a766c674f85df429090989f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7380",
    "kind": "arxiv",
    "version": 1
  }
}