Pith Number

pith:AILUMKJ2

pith:2015:AILUMKJ2GJ6PPXKDRC73A2ITCM

not attested not anchored not stored refs pending

Ballistic Transport and Absolute Continuity of One-Frequency Schr\"{o}dinger Operators

Zhiyan Zhao, Zhiyuan Zhang

arxiv:1512.02195 v2 · 2015-12-07 · math.DS · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AILUMKJ2GJ6PPXKDRC73A2ITCM}

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	2026-05-18T01:19:39.262719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

021746293a327cf7dd4388bfb0691313393c50cb2ecc04df0041edc0af598c23

Aliases

arxiv: 1512.02195 · arxiv_version: 1512.02195v2 · doi: 10.48550/arxiv.1512.02195 · pith_short_12: AILUMKJ2GJ6P · pith_short_16: AILUMKJ2GJ6PPXKD · pith_short_8: AILUMKJ2

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/AILUMKJ2GJ6PPXKDRC73A2ITCM \
  | 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: 021746293a327cf7dd4388bfb0691313393c50cb2ecc04df0041edc0af598c23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10b9b203c38e967eb0fb41f99da34b858611748480225485f8cc16dba4cd29cd",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-12-07T20:32:13Z",
    "title_canon_sha256": "4620ddd69e6e3fe3e15b93bc52868a3fcdeefa8de02cc6e3c0d99c987c32a555"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02195",
    "kind": "arxiv",
    "version": 2
  }
}