Pith Number

pith:YUMSMAW4

pith:2011:YUMSMAW4GH5DEC5ZEFUROWZARB

not attested not anchored not stored refs pending

Paraproducts via $H^\infty$-functional calculus

Dorothee Frey

arxiv:1107.4348 v1 · 2011-07-21 · math.FA · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YUMSMAW4GH5DEC5ZEFUROWZARB}

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	2026-05-18T04:17:12.717882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5192602dc31fa320bb92169175b208878215197e249830370792146211fd07b

Aliases

arxiv: 1107.4348 · arxiv_version: 1107.4348v1 · doi: 10.48550/arxiv.1107.4348 · pith_short_12: YUMSMAW4GH5D · pith_short_16: YUMSMAW4GH5DEC5Z · pith_short_8: YUMSMAW4

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/YUMSMAW4GH5DEC5ZEFUROWZARB \
  | 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: c5192602dc31fa320bb92169175b208878215197e249830370792146211fd07b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32aa52efdca635617ab19410242e0c42f06a587c8689c3dea89de3eb44347d27",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-07-21T19:42:40Z",
    "title_canon_sha256": "3fac2fee46b5fcd8eeeba845fc2296671ba352a7cce1d16aba2f57bc9ebd04da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4348",
    "kind": "arxiv",
    "version": 1
  }
}