Pith Number

pith:Y2Z3QEQG

pith:2003:Y2Z3QEQGHCNRK76TSFBPHRV7E7

not attested not anchored not stored refs pending

A geometric approach to the Littlewood-Paley theory

Igor Rodnianski, Sergiu Klainerman

arxiv:math/0309463 v1 · 2003-09-29 · math.AP · math.CA · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y2Z3QEQGHCNRK76TSFBPHRV7E7}

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	2026-05-18T01:05:28.613210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6b3b81206389b157fd39142f3c6bf27f2c09d1643b030e6523ea57582249ea3

Aliases

arxiv: math/0309463 · arxiv_version: math/0309463v1 · doi: 10.48550/arxiv.math/0309463 · pith_short_12: Y2Z3QEQGHCNR · pith_short_16: Y2Z3QEQGHCNRK76T · pith_short_8: Y2Z3QEQG

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/Y2Z3QEQGHCNRK76TSFBPHRV7E7 \
  | 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: c6b3b81206389b157fd39142f3c6bf27f2c09d1643b030e6523ea57582249ea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c53885327f2b35741746322c973c9a83dd734ae50a1a5cf134b94b91e3521f8a",
    "cross_cats_sorted": [
      "math.CA",
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2003-09-29T17:41:51Z",
    "title_canon_sha256": "c9c2cb03729264b0d81dc3c29e639550aefeaa1a94289be749027741091e5dd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309463",
    "kind": "arxiv",
    "version": 1
  }
}