Pith Number

pith:57RAB5HJ

pith:2022:57RAB5HJ764IW7RHDPMY3KEXQG

not attested not anchored not stored refs pending

Optimal mass normalizability for Gibbs measure associated with NLS on the 2D disc

Tianhao Xian

arxiv:2204.09561 v1 · 2022-04-20 · math.PR · math.AP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{57RAB5HJ764IW7RHDPMY3KEXQG}

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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.

Cited by

1 paper in Pith

Derivation of the focusing $\Phi^6_1$ measure in the optimal mass regime from many-body quantum Gibbs states

Receipt and verification

First computed	2026-07-05T04:16:31.661175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efe200f4e9ffb88b7e271bd98da897819c85dd27e7349cea4edbf7da25ae2691

Aliases

arxiv: 2204.09561 · arxiv_version: 2204.09561v1 · doi: 10.48550/arxiv.2204.09561 · pith_short_12: 57RAB5HJ764I · pith_short_16: 57RAB5HJ764IW7RH · pith_short_8: 57RAB5HJ

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/57RAB5HJ764IW7RHDPMY3KEXQG \
  | 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: efe200f4e9ffb88b7e271bd98da897819c85dd27e7349cea4edbf7da25ae2691

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddc5cb685db0e2a2574f1c05d60df483b2269ef1244cf69fc776f5c9134370df",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-04-20T15:59:21Z",
    "title_canon_sha256": "c51cc08246aa82776670a8d67f192497640f2f4982c6bbc1a9e935bc2c512ab8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2204.09561",
    "kind": "arxiv",
    "version": 1
  }
}