Pith Number

pith:3XOY3CSN

pith:2009:3XOY3CSNPCZE7FVY52C75LJ2GY

not attested not anchored not stored refs pending

Gibbs-like measure for spectrum of a class of one-dimensional Schr\"odinger operator with Sturm potentials

Qing-Hui Liu, Shen Fan, Zhi-Ying Wen

arxiv:0909.2301 v1 · 2009-09-12 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XOY3CSNPCZE7FVY52C75LJ2GY}

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	2026-07-04T15:49:24.366416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dddd8d8a4d78b24f96b8ee85fead3a36191aa81d85ee592f11ab4fd724228fa6

Aliases

arxiv: 0909.2301 · arxiv_version: 0909.2301v1 · doi: 10.48550/arxiv.0909.2301 · pith_short_12: 3XOY3CSNPCZE · pith_short_16: 3XOY3CSNPCZE7FVY · pith_short_8: 3XOY3CSN

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/3XOY3CSNPCZE7FVY52C75LJ2GY \
  | 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: dddd8d8a4d78b24f96b8ee85fead3a36191aa81d85ee592f11ab4fd724228fa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "928875e356020684cc399806b3d94195391889352a1b903eb5595372f185dcdb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-09-12T04:31:00Z",
    "title_canon_sha256": "1b54c0e5e377f07dd9883959cba99369cfd608f93b97ce5a60e189488deb523f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.2301",
    "kind": "arxiv",
    "version": 1
  }
}