Pith Number

pith:GWFQ4J4T

pith:2015:GWFQ4J4TIQVAUVP5UT6H3VQK6T

not attested not anchored not stored refs pending

A priori estimates and weak solutions for the derivative nonlinear Schr\"{o}dinger equation on torus below $H^{1/2}$

Hideo Takaoka

arxiv:1508.03076 v1 · 2015-08-12 · 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{GWFQ4J4TIQVAUVP5UT6H3VQK6T}

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	2026-05-18T01:35:21.803396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

358b0e2793442a0a55fda4fc7dd60af4e76a0c5b5843b98c090ef68d06b6a77c

Aliases

arxiv: 1508.03076 · arxiv_version: 1508.03076v1 · doi: 10.48550/arxiv.1508.03076 · pith_short_12: GWFQ4J4TIQVA · pith_short_16: GWFQ4J4TIQVAUVP5 · pith_short_8: GWFQ4J4T

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/GWFQ4J4TIQVAUVP5UT6H3VQK6T \
  | 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: 358b0e2793442a0a55fda4fc7dd60af4e76a0c5b5843b98c090ef68d06b6a77c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea262edf6e8faee42138e312a4cebeee10a05feb471a6b31ed57fcd53cf53773",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-12T21:38:55Z",
    "title_canon_sha256": "15607f4af040fde93edd18c119494980e7733800b4feece273fe1c60b28db540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03076",
    "kind": "arxiv",
    "version": 1
  }
}