Pith Number

pith:V5VYBDVF

pith:2019:V5VYBDVFUEPXHXKIWPYZJDMM7S

not attested not anchored not stored refs pending

Real variable methods in harmonic analysis and Navier-Stokes equations

Pierre Gilles Lemari\'e-Rieusset

arxiv:1907.03603 v1 · 2019-07-08 · 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{V5VYBDVFUEPXHXKIWPYZJDMM7S}

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	2026-05-17T23:41:14.216656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af6b808ea5a11f73dd48b3f1948d8cfc90aecc8d4baa8b07daf0966b19e706d3

Aliases

arxiv: 1907.03603 · arxiv_version: 1907.03603v1 · doi: 10.48550/arxiv.1907.03603 · pith_short_12: V5VYBDVFUEPX · pith_short_16: V5VYBDVFUEPXHXKI · pith_short_8: V5VYBDVF

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/V5VYBDVFUEPXHXKIWPYZJDMM7S \
  | 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: af6b808ea5a11f73dd48b3f1948d8cfc90aecc8d4baa8b07daf0966b19e706d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ff21a4b189fac73869214c210bbfbc4a0b636320f5ae4210b3a2075cee8c38c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-07-08T13:25:25Z",
    "title_canon_sha256": "5fb9c65cffba1c038b947fe8ecd3357ca3da36faafd7c16257a2e658bcc72d8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.03603",
    "kind": "arxiv",
    "version": 1
  }
}