Pith Number

pith:CPOK4Z5N

pith:2015:CPOK4Z5NF3LP6NTTWZSHXBUIUJ

not attested not anchored not stored refs pending

Global dynamics above the ground state energy for the combined power type nonlinear Schrodinger equations with energy critical growth at low frequencies

Hayato Nawa, Hiroaki Kikuchi, Slim Ibrahim, Takafumi Akahori

arxiv:1510.08034 v2 · 2015-10-27 · 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{CPOK4Z5NF3LP6NTTWZSHXBUIUJ}

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	2026-05-17T23:56:00.898924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13dcae67ad2ed6ff3673b6647b8688a25b9cac2e08ed7cca61542a9a13349660

Aliases

arxiv: 1510.08034 · arxiv_version: 1510.08034v2 · doi: 10.48550/arxiv.1510.08034 · pith_short_12: CPOK4Z5NF3LP · pith_short_16: CPOK4Z5NF3LP6NTT · pith_short_8: CPOK4Z5N

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/CPOK4Z5NF3LP6NTTWZSHXBUIUJ \
  | 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: 13dcae67ad2ed6ff3673b6647b8688a25b9cac2e08ed7cca61542a9a13349660

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47165d83f66802a04b1fe2380c92ffaa03f57f6688ec99aed5ee14a7e9d23c25",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-27T19:24:41Z",
    "title_canon_sha256": "437fb4469cc28e5f5cdd30270add3423cc724ab900cfa8a290e4f1cd885c4687"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08034",
    "kind": "arxiv",
    "version": 2
  }
}