Pith Number

pith:AGFGX2OD

pith:2015:AGFGX2ODD2247CAUQIVLL42QAZ

not attested not anchored not stored refs pending

Spectral Properties of Schr\"odinger Operators With Pattern Sturmian Potentials

David Damanik (Rice University), Qing-Hui Liu (Beijing Institute of Technology), Yan-Hui Qu (Tsinghua University)

arxiv:1511.03834 v1 · 2015-11-12 · math.SP · math-ph · math.DS · 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{AGFGX2ODD2247CAUQIVLL42QAZ}

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	2026-05-18T01:27:06.702175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

018a6be9c31eb5cf8814822ab5f350064d8591251559451b92fe1c1027792393

Aliases

arxiv: 1511.03834 · arxiv_version: 1511.03834v1 · doi: 10.48550/arxiv.1511.03834 · pith_short_12: AGFGX2ODD224 · pith_short_16: AGFGX2ODD2247CAU · pith_short_8: AGFGX2OD

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/AGFGX2ODD2247CAUQIVLL42QAZ \
  | 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: 018a6be9c31eb5cf8814822ab5f350064d8591251559451b92fe1c1027792393

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c85f9e918e59a21b921c9a45ace9f1f5d30a06d64c7601e5850f09ee41c4f7a",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-11-12T10:10:16Z",
    "title_canon_sha256": "b64493ba30fc88d103b79b0bf75e7ae1299c61893dc4a2f92b2d6c1a67f37d66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03834",
    "kind": "arxiv",
    "version": 1
  }
}