Pith Number

pith:M4FXQK7N

pith:2015:M4FXQK7NBK2DIXZUU7GO6LUYJS

not attested not anchored not stored refs pending

Long-Time Asymptotics for the integrable discrete nonlinear Schr\"odinger equation: The Focusing Case

Hideshi Yamane

arxiv:1512.01760 v4 · 2015-12-06 · math-ph · 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{M4FXQK7NBK2DIXZUU7GO6LUYJS}

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	2026-05-18T01:02:04.748413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

670b782bed0ab4345f34a7ccef2e984c8003d94a4a6bf8e0b2bad10bd9431bf0

Aliases

arxiv: 1512.01760 · arxiv_version: 1512.01760v4 · doi: 10.48550/arxiv.1512.01760 · pith_short_12: M4FXQK7NBK2D · pith_short_16: M4FXQK7NBK2DIXZU · pith_short_8: M4FXQK7N

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/M4FXQK7NBK2DIXZUU7GO6LUYJS \
  | 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: 670b782bed0ab4345f34a7ccef2e984c8003d94a4a6bf8e0b2bad10bd9431bf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fb40acbe36297e8238c1fb9b5a50fbba539afb79773ecc4b5e7a92efe4bbe99",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-12-06T08:59:40Z",
    "title_canon_sha256": "9a981a7373074009fd3107fe5d4522f33bf079b3b511f2f5676e97ae6ffe445d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01760",
    "kind": "arxiv",
    "version": 4
  }
}