Pith Number

pith:TJR2JR5Q

pith:2001:TJR2JR5QTFGH5CRH7XKEAFBNCK

not attested not anchored not stored refs pending

The Gravitational Million-Body Problem

Douglas C. Heggie

arxiv:astro-ph/0111045 v1 · 2001-11-02 · astro-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{TJR2JR5QTFGH5CRH7XKEAFBNCK}

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.

Cited by

1 paper in Pith

Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching

Receipt and verification

First computed	2026-07-04T14:11:37.131914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a63a4c7b0994c7e8a27fdd440142d12a33bc607d6b9013897695d08c657582b

Aliases

arxiv: astro-ph/0111045 · arxiv_version: astro-ph/0111045v1 · doi: 10.48550/arxiv.astro-ph/0111045 · pith_short_12: TJR2JR5QTFGH · pith_short_16: TJR2JR5QTFGH5CRH · pith_short_8: TJR2JR5Q

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/TJR2JR5QTFGH5CRH7XKEAFBNCK \
  | 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: 9a63a4c7b0994c7e8a27fdd440142d12a33bc607d6b9013897695d08c657582b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74b12908e217e3fc1e43c9e9e7ed705417cbcdaab7d46664ce90ce36964b28e8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2001-11-02T13:39:28Z",
    "title_canon_sha256": "c793edbad1e568be563fb70e92bc6f9b26664d969b0048e41978fb47b77b320f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0111045",
    "kind": "arxiv",
    "version": 1
  }
}