Pith Number

pith:2T5N3AFK

pith:2012:2T5N3AFKYVFULHBD6KLHLTJYDX

not attested not anchored not stored refs pending

Comment on `The tan {\theta} theorem with relaxed conditions', by Y. Nakatsukasa

Alexander K. Motovilov

arxiv:1204.4441 v2 · 2012-04-19 · math.SP · math.NA · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2T5N3AFKYVFULHBD6KLHLTJYDX}

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	2026-05-18T03:42:13.233919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4fadd80aac54b459c23f29675cd381dedca6aa6535f466631d3523d4c0e07a3

Aliases

arxiv: 1204.4441 · arxiv_version: 1204.4441v2 · doi: 10.48550/arxiv.1204.4441 · pith_short_12: 2T5N3AFKYVFU · pith_short_16: 2T5N3AFKYVFULHBD · pith_short_8: 2T5N3AFK

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/2T5N3AFKYVFULHBD6KLHLTJYDX \
  | 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: d4fadd80aac54b459c23f29675cd381dedca6aa6535f466631d3523d4c0e07a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6237258d741ec78195405c26a33a80f28b716793b95e35fee3bf064d90d292f",
    "cross_cats_sorted": [
      "math.NA",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-04-19T19:27:24Z",
    "title_canon_sha256": "97e1946367cd696a6fdedfcccd68a3462fcc1229c7ed47947d72d49640c7274f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4441",
    "kind": "arxiv",
    "version": 2
  }
}