Pith Number

pith:3YX3V7IP

pith:1999:3YX3V7IPMNSXPMRNMBJ5BLHIFZ

not attested not anchored not stored refs pending

Sharp Lorentz space estimates for rough operators

Andreas Seeger, Terence Tao

arxiv:math/9912098 v1 · 1999-12-13 · 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{3YX3V7IPMNSXPMRNMBJ5BLHIFZ}

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	2026-07-04T14:41:31.590996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de2fbafd0f636577b22d6053d0ace82e7b4abcc887624df0f0e18dfe9835211a

Aliases

arxiv: math/9912098 · arxiv_version: math/9912098v1 · doi: 10.48550/arxiv.math/9912098 · pith_short_12: 3YX3V7IPMNSX · pith_short_16: 3YX3V7IPMNSXPMRN · pith_short_8: 3YX3V7IP

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/3YX3V7IPMNSXPMRNMBJ5BLHIFZ \
  | 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: de2fbafd0f636577b22d6053d0ace82e7b4abcc887624df0f0e18dfe9835211a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a88e5fb85ba373595474162445f86c55d4384d9c2f3e412f32454af21dbbeb51",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "1999-12-13T02:23:55Z",
    "title_canon_sha256": "0fe25394673592c7176dbca1e706646d6986b066c0d275a57cf1a1e8aada0a11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912098",
    "kind": "arxiv",
    "version": 1
  }
}