Pith Number

pith:X7T7DH2T

pith:2011:X7T7DH2TZVAY5AF4AGNGA5SHMT

not attested not anchored not stored refs pending

Kohn's theorem and Newton-Hooke symmetry for Hill's equations

G. W. Gibbons, P. A. Horvathy, P. M. Zhang

arxiv:1112.4793 v3 · 2011-12-20 · hep-th · astro-ph.GA · gr-qc · math-ph · 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{X7T7DH2TZVAY5AF4AGNGA5SHMT}

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	2026-05-18T04:01:37.732982Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfe7f19f53cd418e80bc019a60764764c31c6ad767caa01b82efb96eda7fca52

Aliases

arxiv: 1112.4793 · arxiv_version: 1112.4793v3 · doi: 10.48550/arxiv.1112.4793 · pith_short_12: X7T7DH2TZVAY · pith_short_16: X7T7DH2TZVAY5AF4 · pith_short_8: X7T7DH2T

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/X7T7DH2TZVAY5AF4AGNGA5SHMT \
  | 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: bfe7f19f53cd418e80bc019a60764764c31c6ad767caa01b82efb96eda7fca52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8c69d6097a9a8b55f88cd4a0b499f16515e566aaa647a166be325a304151c80",
    "cross_cats_sorted": [
      "astro-ph.GA",
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2011-12-20T18:30:18Z",
    "title_canon_sha256": "bb0f25dd01b06c6807b08443ef62d174bd1bf7d9148ae292606daa16d65e94b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4793",
    "kind": "arxiv",
    "version": 3
  }
}