Pith Number

pith:VIZLN7AJ

pith:2017:VIZLN7AJ7C3STNB6DZ5K635GEI

not attested not anchored not stored refs pending

Finite energy of generalized suitable weak solutions to the Navier-Stokes equations and Liouville-type theorems in two dimensional domains

Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi

arxiv:1708.07618 v1 · 2017-08-25 · 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{VIZLN7AJ7C3STNB6DZ5K635GEI}

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	2026-05-18T00:16:08.771936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa32b6fc09f8b729b43e1e7aaf6fa622179286bfc019c9192ae2131438352e34

Aliases

arxiv: 1708.07618 · arxiv_version: 1708.07618v1 · doi: 10.48550/arxiv.1708.07618 · pith_short_12: VIZLN7AJ7C3S · pith_short_16: VIZLN7AJ7C3STNB6 · pith_short_8: VIZLN7AJ

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/VIZLN7AJ7C3STNB6DZ5K635GEI \
  | 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: aa32b6fc09f8b729b43e1e7aaf6fa622179286bfc019c9192ae2131438352e34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "370594bd409837b16afe5b6bd94677ee1a63401cedb4d262a651227da4bac45b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-08-25T06:02:02Z",
    "title_canon_sha256": "48a095ce77d43ddba4aba1d5e643d0f30ca9f7584ef02f65e947c6462c118f16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.07618",
    "kind": "arxiv",
    "version": 1
  }
}