Pith Number

pith:CLC4FA5S

pith:2011:CLC4FA5SLT4RKHGXHNA2UV3Y5S

not attested not anchored not stored refs pending

Pair correlation of angles between reciprocal geodesics on the modular surface

Alexandru A. Popa, Alexandru Zaharescu, Florin P. Boca, Vicentiu Pasol

arxiv:1102.0328 v4 · 2011-02-02 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLC4FA5SLT4RKHGXHNA2UV3Y5S}

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	2026-05-18T01:22:29.131792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12c5c283b25cf9151cd73b41aa5778ec875e36b738d6676bc26b26f7ed666fcb

Aliases

arxiv: 1102.0328 · arxiv_version: 1102.0328v4 · doi: 10.48550/arxiv.1102.0328 · pith_short_12: CLC4FA5SLT4R · pith_short_16: CLC4FA5SLT4RKHGX · pith_short_8: CLC4FA5S

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/CLC4FA5SLT4RKHGXHNA2UV3Y5S \
  | 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: 12c5c283b25cf9151cd73b41aa5778ec875e36b738d6676bc26b26f7ed666fcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e520efef787a1a3080b0d36c90c798199986ae4960b7e01262930a21895a5dfa",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-02T00:11:47Z",
    "title_canon_sha256": "f55847e91f325ad9f06fcbbe008546a2b91ddc714c9f94d7b92c3ca3d493385f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0328",
    "kind": "arxiv",
    "version": 4
  }
}