Pith Number

pith:7NDUNBUU

pith:2026:7NDUNBUUH2KZYIESFIDVNFOKGE

not attested not anchored not stored refs pending

Sharp Broken-Power Lorentz Estimates for Fractional Powers of Radial Schr\"odinger Operators with Inverse-Square Asymptotics

Haochen Liu, Hongyan Zhou, Qinghao Yu

arxiv:2607.11280 v1 · 2026-07-13 · math.AP · math-ph · math.CA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NDUNBUUH2KZYIESFIDVNFOKGE}

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	2026-07-14T01:22:26.434122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb474686943e959c20922a075695ca313dc01c06defef2e1ece065149acf80c4

Aliases

arxiv: 2607.11280 · arxiv_version: 2607.11280v1 · doi: 10.48550/arxiv.2607.11280 · pith_short_12: 7NDUNBUUH2KZ · pith_short_16: 7NDUNBUUH2KZYIES · pith_short_8: 7NDUNBUU

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/7NDUNBUUH2KZYIESFIDVNFOKGE \
  | 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: fb474686943e959c20922a075695ca313dc01c06defef2e1ece065149acf80c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54a8bd4aa19c9ff4158b167c81600f792eeb8a303e4faef910432699f54ab39d",
    "cross_cats_sorted": [
      "math-ph",
      "math.CA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-13T09:00:20Z",
    "title_canon_sha256": "942534bb3d5cdc785c9269e3cbe14d441cc732becf15fccd56ab88b542cce8f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11280",
    "kind": "arxiv",
    "version": 1
  }
}