Pith Number

pith:VAMUXSJ5

pith:2015:VAMUXSJ5ECMTXPGAGAKA2SWO34

not attested not anchored not stored refs pending

Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schr\"odinger Equation

Zhiyan Zhao

arxiv:1507.08909 v4 · 2015-07-31 · math-ph · math.AP · math.MP · 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{VAMUXSJ5ECMTXPGAGAKA2SWO34}

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	2026-05-18T01:18:57.307290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8194bc93d20993bbcc030140d4acedf146cdc14d114c09472187c95733f35e8

Aliases

arxiv: 1507.08909 · arxiv_version: 1507.08909v4 · doi: 10.48550/arxiv.1507.08909 · pith_short_12: VAMUXSJ5ECMT · pith_short_16: VAMUXSJ5ECMTXPGA · pith_short_8: VAMUXSJ5

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/VAMUXSJ5ECMTXPGAGAKA2SWO34 \
  | 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: a8194bc93d20993bbcc030140d4acedf146cdc14d114c09472187c95733f35e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87cc7b34a6d0219ceedd71abd09f138cdfc70e8cb77b98e7a41dbf9acc28e6f4",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-07-31T15:09:38Z",
    "title_canon_sha256": "76768cde0e51370dc3521db1ccb2d9c8dd36e16bf5d712edf05154a83e645dc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08909",
    "kind": "arxiv",
    "version": 4
  }
}