Pith Number

pith:NATDRCZY

pith:2025:NATDRCZYUQHE7SHB7SDDPM3QYD

not attested not anchored not stored refs pending

Qualitative analysis of multi-peak solutions for Nonlinear Schr\"{o}dinger equations with nearly critical Sobolev exponents

Huafei Xie, Pingping Yang, Shuying Tian, Zhongyuan Liu

arxiv:2512.18663 v1 · 2025-12-21 · 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{NATDRCZYUQHE7SHB7SDDPM3QYD}

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	2026-06-04T17:10:11.448706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6826388b38a40e4fc8e1fc8637b370c0ee05df8253e5eea0f3172e4a54bb2bcd

Aliases

arxiv: 2512.18663 · arxiv_version: 2512.18663v1 · doi: 10.48550/arxiv.2512.18663 · pith_short_12: NATDRCZYUQHE · pith_short_16: NATDRCZYUQHE7SHB · pith_short_8: NATDRCZY

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/NATDRCZYUQHE7SHB7SDDPM3QYD \
  | 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: 6826388b38a40e4fc8e1fc8637b370c0ee05df8253e5eea0f3172e4a54bb2bcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ef4be1655d916804a90d0c5bc45656fb29813d844af4f5417955a349b3a5b5e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-12-21T09:21:30Z",
    "title_canon_sha256": "7e382d13c68fcb4fac723ced22cfae4b166593c431bf2718666ed38d11b64f35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.18663",
    "kind": "arxiv",
    "version": 1
  }
}