Pith Number

pith:I4P3TFQY

pith:2026:I4P3TFQY7OIDVKWPZOKAOH4WHN

not attested not anchored not stored refs pending

Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges

Hugo Beir\~ao da Veiga, Jiaqi Yang

arxiv:2608.11553 v1 · 2026-08-12 · 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{I4P3TFQY7OIDVKWPZOKAOH4WHN}

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	2026-08-13T00:22:10.252254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8

Aliases

arxiv: 2608.11553 · arxiv_version: 2608.11553v1 · doi: 10.48550/arxiv.2608.11553 · pith_short_12: I4P3TFQY7OID · pith_short_16: I4P3TFQY7OIDVKWP · pith_short_8: I4P3TFQY

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/I4P3TFQY7OIDVKWPZOKAOH4WHN \
  | 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: 471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee98c8e0874a5b575b0c09087d9505c2b7bc50d8951e5524753297e316dcc68",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-12T01:40:31Z",
    "title_canon_sha256": "fa0f14fbbece6f8ce3f9c2b57d6b07563b929c67bbda89f126c2fa650665ef53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.11553",
    "kind": "arxiv",
    "version": 1
  }
}