Pith Number

pith:B75YQV5I

pith:2015:B75YQV5ILXHLQWIEFVYMA7VUBG

not attested not anchored not stored refs pending

Refined and Microlocal Kakeya-Nikodym Bounds of Eigenfunctions in Higher Dimensions

Christopher D. Sogge, Matthew D. Blair

arxiv:1510.07724 v3 · 2015-10-26 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B75YQV5ILXHLQWIEFVYMA7VUBG}

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	2026-05-18T00:43:39.845935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ffb8857a85dceb859042d70c07eb409af46232ed0f4b869b55597e80231e6b8

Aliases

arxiv: 1510.07724 · arxiv_version: 1510.07724v3 · doi: 10.48550/arxiv.1510.07724 · pith_short_12: B75YQV5ILXHL · pith_short_16: B75YQV5ILXHLQWIE · pith_short_8: B75YQV5I

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/B75YQV5ILXHLQWIEFVYMA7VUBG \
  | 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: 0ffb8857a85dceb859042d70c07eb409af46232ed0f4b869b55597e80231e6b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af0fe34423922c15e0808998296f6291687040176d6b248404476f5058e5f935",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-26T23:51:18Z",
    "title_canon_sha256": "03965e0fe61de124938c3722298c9d0d63504e089d24e040eb01edcba911badf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07724",
    "kind": "arxiv",
    "version": 3
  }
}