Pith Number

pith:O7G7LMGP

pith:2007:O7G7LMGPNCV5NRID4DD57UVDJS

not attested not anchored not stored refs pending

An Extrapolation of Operator Valued Dyadic Paraproducts

Tao Mei

arxiv:0709.4229 v1 · 2007-09-26 · 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{O7G7LMGPNCV5NRID4DD57UVDJS}

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	2026-05-18T02:58:12.277396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77cdf5b0cf68abd6c503e0c7dfd2a34cbf12a86df68382dfbc3aade1e90a1334

Aliases

arxiv: 0709.4229 · arxiv_version: 0709.4229v1 · doi: 10.48550/arxiv.0709.4229 · pith_short_12: O7G7LMGPNCV5 · pith_short_16: O7G7LMGPNCV5NRID · pith_short_8: O7G7LMGP

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/O7G7LMGPNCV5NRID4DD57UVDJS \
  | 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: 77cdf5b0cf68abd6c503e0c7dfd2a34cbf12a86df68382dfbc3aade1e90a1334

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1b615732c10ab6ad53a2f1c44daf31804337c0cdccde9db744d65bfcbae2ea6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2007-09-26T18:12:08Z",
    "title_canon_sha256": "f48c92049acc497783331237d7e70564d82f0733fb8d93108427896d7e0a260a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.4229",
    "kind": "arxiv",
    "version": 1
  }
}