Pith Number

pith:7RK2QKYR

pith:2017:7RK2QKYR6PTVCMFHJIYFCSRFHW

not attested not anchored not stored refs pending

On the focusing mass-critical nonlinear fourth-order Schr\"odinger equation below the energy space

Van Duong Dinh

arxiv:1706.09304 v2 · 2017-06-27 · 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{7RK2QKYR6PTVCMFHJIYFCSRFHW}

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	2026-05-18T00:32:50.469032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc55a82b11f3e75130a74a30514a253da2f156cbc0235b5c4e0a6b6b951acfaf

Aliases

arxiv: 1706.09304 · arxiv_version: 1706.09304v2 · doi: 10.48550/arxiv.1706.09304 · pith_short_12: 7RK2QKYR6PTV · pith_short_16: 7RK2QKYR6PTVCMFH · pith_short_8: 7RK2QKYR

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/7RK2QKYR6PTVCMFHJIYFCSRFHW \
  | 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: fc55a82b11f3e75130a74a30514a253da2f156cbc0235b5c4e0a6b6b951acfaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7a1b263de8f7bdf4657a80d524b2594346ad0675729aaeb98f70cdc4eb52ada",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-06-27T17:55:00Z",
    "title_canon_sha256": "bb8d64c499506a901192d2fc3b49214536e2ad861ecc48221bfe556fde33a8f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09304",
    "kind": "arxiv",
    "version": 2
  }
}