Pith Number

pith:ACAQMHCI

pith:2001:ACAQMHCI5BHCOPQLWDYNAJ7CRF

not attested not anchored not stored refs pending

An Elementary Proof of Lyapunov Exponent Pairing for Hard-Sphere Systems at Constant Kinetic Energy

Debabrata Panja

arxiv:nlin/0107048 v4 · 2001-07-21 · nlin.CD · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ACAQMHCI5BHCOPQLWDYNAJ7CRF}

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	2026-05-18T01:38:21.782436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0081061c48e84e273e0bb0f0d027e2895b7064806bb4a7971712bbda63eccc5d

Aliases

arxiv: nlin/0107048 · arxiv_version: nlin/0107048v4 · doi: 10.48550/arxiv.nlin/0107048 · pith_short_12: ACAQMHCI5BHC · pith_short_16: ACAQMHCI5BHCOPQL · pith_short_8: ACAQMHCI

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/ACAQMHCI5BHCOPQLWDYNAJ7CRF \
  | 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: 0081061c48e84e273e0bb0f0d027e2895b7064806bb4a7971712bbda63eccc5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "254320f94344b33d20e3c60a6453c761a944eceffe81f811d1dfe16d560a9854",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "",
    "primary_cat": "nlin.CD",
    "submitted_at": "2001-07-21T08:43:26Z",
    "title_canon_sha256": "02c7f6b22c70d41bb949594c6526108df62ed92dfa551acb8bb1aa38d77e8db6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "nlin/0107048",
    "kind": "arxiv",
    "version": 4
  }
}