Pith Number

pith:TCYKD6NT

pith:2026:TCYKD6NTMG74JMN6JYMPUW64FN

not attested not anchored not stored refs pending

The effect of geometric focusing on dispersive estimates for Schr\"odinger and wave equations

Junyong Zhang, Qiuye Jia

arxiv:2606.09280 v1 · 2026-06-08 · math.AP · 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{TCYKD6NTMG74JMN6JYMPUW64FN}

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	2026-06-09T02:08:12.038365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98b0a1f9b361bfc4b1be4e18fa5bdc2b775260d9bb18b16009e117ccab5191b2

Aliases

arxiv: 2606.09280 · arxiv_version: 2606.09280v1 · doi: 10.48550/arxiv.2606.09280 · pith_short_12: TCYKD6NTMG74 · pith_short_16: TCYKD6NTMG74JMN6 · pith_short_8: TCYKD6NT

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/TCYKD6NTMG74JMN6JYMPUW64FN \
  | 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: 98b0a1f9b361bfc4b1be4e18fa5bdc2b775260d9bb18b16009e117ccab5191b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6ae83b6b3d08e117f0b13615c53731557c927ad581aa18ff85b9bda2ef4f20d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-08T09:46:06Z",
    "title_canon_sha256": "59f6034b477e119455b226876931a00570624adb80731adf084f984f5ddd7d31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09280",
    "kind": "arxiv",
    "version": 1
  }
}