Pith Number

pith:OYRP6QNH

pith:2013:OYRP6QNHRLDWGVTQ4C7KJATV22

not attested not anchored not stored refs pending

A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

Roberto Castelli

arxiv:1309.1594 v1 · 2013-09-06 · 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{OYRP6QNHRLDWGVTQ4C7KJATV22}

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	2026-05-18T03:13:59.111748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7622ff41a78ac7635670e0bea48275d6b35bac89b976ace6a59ebb16ddec4172

Aliases

arxiv: 1309.1594 · arxiv_version: 1309.1594v1 · doi: 10.48550/arxiv.1309.1594 · pith_short_12: OYRP6QNHRLDW · pith_short_16: OYRP6QNHRLDWGVTQ · pith_short_8: OYRP6QNH

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/OYRP6QNHRLDWGVTQ4C7KJATV22 \
  | 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: 7622ff41a78ac7635670e0bea48275d6b35bac89b976ace6a59ebb16ddec4172

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f4353d1fb909ed2bf19dcdb90f629b29bf684f81eaa85a4b53076c59fd47320",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-09-06T10:53:13Z",
    "title_canon_sha256": "b4cdcc1592c76533c15cc0fd1d8be0b4f9cec93327e2501edcf440982cf951b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1594",
    "kind": "arxiv",
    "version": 1
  }
}