Pith Number

pith:5J4M3PQ2

pith:2026:5J4M3PQ2Q3G2Y6T2ZQHTJZN5VO

not attested not anchored not stored refs pending

Fractal Tur\'{a}n-Nazarov Inequality and Observability for Schr\"{o}dinger Equations

Jiaqi Yu, Shanlin Huang

arxiv:2607.17505 v1 · 2026-07-20 · 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{5J4M3PQ2Q3G2Y6T2ZQHTJZN5VO}

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	2026-07-21T01:21:49.092916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea78cdbe1a86cdac7a7acc0f34e5bdabb1b71513251e47c1550195ba121b4148

Aliases

arxiv: 2607.17505 · arxiv_version: 2607.17505v1 · doi: 10.48550/arxiv.2607.17505 · pith_short_12: 5J4M3PQ2Q3G2 · pith_short_16: 5J4M3PQ2Q3G2Y6T2 · pith_short_8: 5J4M3PQ2

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/5J4M3PQ2Q3G2Y6T2ZQHTJZN5VO \
  | 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: ea78cdbe1a86cdac7a7acc0f34e5bdabb1b71513251e47c1550195ba121b4148

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "210f8a94580b7d9809412ade2148bac088a06a489063a056e779989a535a51a2",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-20T03:21:44Z",
    "title_canon_sha256": "31c32dbde6c2c64e27d17a96c89b8b1e207bd38fc68ce206851e7560e6627842"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17505",
    "kind": "arxiv",
    "version": 1
  }
}