Pith Number

pith:3U6T55J4

pith:2024:3U6T55J4WVOBC26DAVUBFDN6K2

not attested not anchored not stored refs pending

Normalized solutions on large smooth domains to the Schr\"{o}dinger equations with potential and combined nonlinearities: The Sobolev critical case

Xiaolu Lin, Yanjun Liu, Zongyan Lv

arxiv:2412.03296 v2 · 2024-12-04 · 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{3U6T55J4WVOBC26DAVUBFDN6K2}

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	2026-07-05T09:56:37.936327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd3d3ef53cb55c116bc30568128dbe568cbd2f5bb8e1761de9aec2a69cbd6f13

Aliases

arxiv: 2412.03296 · arxiv_version: 2412.03296v2 · doi: 10.48550/arxiv.2412.03296 · pith_short_12: 3U6T55J4WVOB · pith_short_16: 3U6T55J4WVOBC26D · pith_short_8: 3U6T55J4

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/3U6T55J4WVOBC26DAVUBFDN6K2 \
  | 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: dd3d3ef53cb55c116bc30568128dbe568cbd2f5bb8e1761de9aec2a69cbd6f13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35c98358cbf14bb2f6a11dbbe1f113107a5e410883671ea60d78dba91b3e0b8d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-04T13:15:27Z",
    "title_canon_sha256": "313a6ac34250e6fa86af4b78cf8327baf028df68cef5713376acd2d86899b5dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03296",
    "kind": "arxiv",
    "version": 2
  }
}