Pith Number

pith:336NHVU4

pith:2010:336NHVU4LYA4HGL7TJFHJPLMHL

not attested not anchored not stored refs pending

The TAN $2\Theta$ Theorem for Indefinite Quadratic Forms

Konstantin A. Makarov, Kre\v{s}imir Veseli\'c, Luka Grubi\v{s}i\'c, Vadim Kostrykin

arxiv:1006.3190 v1 · 2010-06-16 · math.SP · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{336NHVU4LYA4HGL7TJFHJPLMHL}

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	2026-05-18T03:35:14.509143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

defcd3d69c5e01c3997f9a4a74bd6c3ac6d1bc9b54678accd010ec283a84f770

Aliases

arxiv: 1006.3190 · arxiv_version: 1006.3190v1 · doi: 10.48550/arxiv.1006.3190 · pith_short_12: 336NHVU4LYA4 · pith_short_16: 336NHVU4LYA4HGL7 · pith_short_8: 336NHVU4

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/336NHVU4LYA4HGL7TJFHJPLMHL \
  | 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: defcd3d69c5e01c3997f9a4a74bd6c3ac6d1bc9b54678accd010ec283a84f770

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7df6750544c0d7e6333ee07e2a55e913fb641857f938362154cb0f15fc74633d",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-06-16T12:13:13Z",
    "title_canon_sha256": "a07f9f045467cd5ed68c30d83cec0a7bceb7651aaf0b0c7c0d00ae6e45985231"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3190",
    "kind": "arxiv",
    "version": 1
  }
}