Pith Number

pith:TJAPXE5L

pith:2025:TJAPXE5LASPNTWFINJXUSOOLMW

not attested not anchored not stored refs pending

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation

Zisu Zhao

arxiv:2507.06237 v2 · 2025-06-18 · math.DG · 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{TJAPXE5LASPNTWFINJXUSOOLMW}

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	2026-07-05T12:04:37.417024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a40fb93ab049ed9d8a86a6f4939cb65990aae2fbf51981113d2e427ef1fd882

Aliases

arxiv: 2507.06237 · arxiv_version: 2507.06237v2 · doi: 10.48550/arxiv.2507.06237 · pith_short_12: TJAPXE5LASPN · pith_short_16: TJAPXE5LASPNTWFI · pith_short_8: TJAPXE5L

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/TJAPXE5LASPNTWFINJXUSOOLMW \
  | 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: 9a40fb93ab049ed9d8a86a6f4939cb65990aae2fbf51981113d2e427ef1fd882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ae9abf5736446b3ca4db014807bfbb05442a1b927cb0b95f8e25313f30f758e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-06-18T05:57:52Z",
    "title_canon_sha256": "3a166120cd361bb27a2d57d5377c8c456a632b681cb71db2adc441ec9dd90f0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06237",
    "kind": "arxiv",
    "version": 2
  }
}