Pith Number

pith:QF2575R6

pith:2014:QF2575R6MMFDQQCUIWJ3Z46VHV

not attested not anchored not stored refs pending

Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions

Christopher D. Sogge, Matthew D. Blair

arxiv:1409.1286 v1 · 2014-09-03 · 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{QF2575R6MMFDQQCUIWJ3Z46VHV}

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	2026-05-18T01:22:21.806227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8175dff63e630a3840544593bcf3d53d46937d0c71d15dc2c91187c9ba9c9855

Aliases

arxiv: 1409.1286 · arxiv_version: 1409.1286v1 · doi: 10.48550/arxiv.1409.1286 · pith_short_12: QF2575R6MMFD · pith_short_16: QF2575R6MMFDQQCU · pith_short_8: QF2575R6

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/QF2575R6MMFDQQCUIWJ3Z46VHV \
  | 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: 8175dff63e630a3840544593bcf3d53d46937d0c71d15dc2c91187c9ba9c9855

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b9bdce7db7def7672befcc34182f4700d99484ae65bef77b794788624704e5b",
    "cross_cats_sorted": [
      "math.CA",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-09-03T23:43:35Z",
    "title_canon_sha256": "f6ba9fc9ea6d9f1859ddb1d2d39057d4b78a5baf2e7423b603547b67e34a16a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.1286",
    "kind": "arxiv",
    "version": 1
  }
}