Pith Number

pith:OTEXTNAF

pith:2026:OTEXTNAFKV3P5DPQAUSLMMFFQ4

not attested not anchored not stored refs pending

Fractional Sobolev embeddings on noncommutative torus

D. Zanin, F. Sukochev, K. Tulenov, R. Tastankul

arxiv:2606.03185 v1 · 2026-06-02 · 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{OTEXTNAFKV3P5DPQAUSLMMFFQ4}

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	2026-06-03T01:05:34.343868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74c979b4055576fe8df00524b630a5873872feea177ae3721ab7a9599af0de2b

Aliases

arxiv: 2606.03185 · arxiv_version: 2606.03185v1 · doi: 10.48550/arxiv.2606.03185 · pith_short_12: OTEXTNAFKV3P · pith_short_16: OTEXTNAFKV3P5DPQ · pith_short_8: OTEXTNAF

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/OTEXTNAFKV3P5DPQAUSLMMFFQ4 \
  | 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: 74c979b4055576fe8df00524b630a5873872feea177ae3721ab7a9599af0de2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea120014df87fec5a593b9ef89aaf794bd8b5dd7cd77e53f86d2c5998418716b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-02T05:42:56Z",
    "title_canon_sha256": "0f57c7981a48cb0dc89f5a8408d5d1a7901a8e61d69b325d73d7a5b8ed2f5cfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03185",
    "kind": "arxiv",
    "version": 1
  }
}