Pith Number

pith:FXDBU4P7

pith:2013:FXDBU4P76U6YNCD2YURS3F2BI2

not attested not anchored not stored refs pending

On Schr\"odinger equations with periodic potentials and with nonperiodic nonlinearities

Fei Fang

arxiv:1307.7320 v2 · 2013-07-27 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FXDBU4P76U6YNCD2YURS3F2BI2}

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	2026-05-18T03:08:36.511481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dc61a71fff53d86887ac5232d9741469e1387834e763a9377daa4a84df614c9

Aliases

arxiv: 1307.7320 · arxiv_version: 1307.7320v2 · doi: 10.48550/arxiv.1307.7320 · pith_short_12: FXDBU4P76U6Y · pith_short_16: FXDBU4P76U6YNCD2 · pith_short_8: FXDBU4P7

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/FXDBU4P76U6YNCD2YURS3F2BI2 \
  | 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: 2dc61a71fff53d86887ac5232d9741469e1387834e763a9377daa4a84df614c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bdfa12e08db1a6ee3de57e7cb7214784ddf56651a9368662bdc6a7fcd75166a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-27T23:11:40Z",
    "title_canon_sha256": "2b5007cf0d63d862771024b383c7f9149a3e1a898bdc470291460da5b27f712c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7320",
    "kind": "arxiv",
    "version": 2
  }
}