Pith Number

pith:ZMYCYDG4

pith:2017:ZMYCYDG4ZW5QCL7FWGTZTX6RL3

not attested not anchored not stored refs pending

Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime

Fan Yang

arxiv:1708.03085 v1 · 2017-08-10 · 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{ZMYCYDG4ZW5QCL7FWGTZTX6RL3}

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	2026-05-18T00:38:14.835240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb302c0cdccdbb012fe5b1a799dfd15ef278c07fefc6840cb586487d3fbc774c

Aliases

arxiv: 1708.03085 · arxiv_version: 1708.03085v1 · doi: 10.48550/arxiv.1708.03085 · pith_short_12: ZMYCYDG4ZW5Q · pith_short_16: ZMYCYDG4ZW5QCL7F · pith_short_8: ZMYCYDG4

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/ZMYCYDG4ZW5QCL7FWGTZTX6RL3 \
  | 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: cb302c0cdccdbb012fe5b1a799dfd15ef278c07fefc6840cb586487d3fbc774c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cc3612eeb74ee77b89c8955553f02e726d5d67bd48e62686e330a7cc0e342b2",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-08-10T06:07:53Z",
    "title_canon_sha256": "f06db0609fa35c4da6e39e6eccd38b2de14f3052ebb40c760def7aec83e0434d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.03085",
    "kind": "arxiv",
    "version": 1
  }
}