Pith Number

pith:7ECDOL3Y

pith:2026:7ECDOL3YX5GU5IG4HQMG5Y665P

not attested not anchored not stored refs pending

Sharp mass-threshold for Dancer-type solutions of the focusing mass-critical NLS on $\Bbb R^d\times\Bbb T$

Yongming Luo

arxiv:2606.05707 v1 · 2026-06-04 · 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{7ECDOL3YX5GU5IG4HQMG5Y665P}

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	2026-06-05T01:14:59.888610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f904372f78bf4d4ea0dc3c186ee3deebd6ba9085581cb9508df78d917e311d88

Aliases

arxiv: 2606.05707 · arxiv_version: 2606.05707v1 · doi: 10.48550/arxiv.2606.05707 · pith_short_12: 7ECDOL3YX5GU · pith_short_16: 7ECDOL3YX5GU5IG4 · pith_short_8: 7ECDOL3Y

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/7ECDOL3YX5GU5IG4HQMG5Y665P \
  | 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: f904372f78bf4d4ea0dc3c186ee3deebd6ba9085581cb9508df78d917e311d88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dab69cc29d795a79256a0f84ee943427300bdc1183eb238433769aa9e88b2c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-04T04:58:10Z",
    "title_canon_sha256": "e788bd3d43ac27cbe331c2c79ba6c230a9fbc8da772e501c6d81817721630682"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05707",
    "kind": "arxiv",
    "version": 1
  }
}