Pith Number

pith:DO3KPA4W

pith:2016:DO3KPA4WNUAJNOM2E57FIT5AHF

not attested not anchored not stored refs pending

Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

Changxing Miao, Christopher D. Sogge, Jianwei Yang, Yakun Xi

arxiv:1602.06936 v2 · 2016-02-22 · 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{DO3KPA4WNUAJNOM2E57FIT5AHF}

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	2026-05-18T00:49:52.415014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bb6a783966d0096b99a277e544fa0396ea903dea1f3eb851463e2734c514688

Aliases

arxiv: 1602.06936 · arxiv_version: 1602.06936v2 · doi: 10.48550/arxiv.1602.06936 · pith_short_12: DO3KPA4WNUAJ · pith_short_16: DO3KPA4WNUAJNOM2 · pith_short_8: DO3KPA4W

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/DO3KPA4WNUAJNOM2E57FIT5AHF \
  | 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: 1bb6a783966d0096b99a277e544fa0396ea903dea1f3eb851463e2734c514688

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fd4d894a2205dbe7107766e4bed9a33810b133a7bfe61c4c4dd767a4545392f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-02-22T20:53:22Z",
    "title_canon_sha256": "0d7859e9565ffa5866bbbed2d0da529f1855b17f1e09662d25e4e246b1b32d1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.06936",
    "kind": "arxiv",
    "version": 2
  }
}