Pith Number

pith:X3QR3URS

pith:2006:X3QR3URS2R7NFK5UMW7RXFBPLH

not attested not anchored not stored refs pending

Breaking the duality in the return times theorem

Christoph Thiele, Ciprian Demeter, Michael Lacey, Terence Tao

arxiv:math/0601455 v2 · 2006-01-18 · math.DS · 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{X3QR3URS2R7NFK5UMW7RXFBPLH}

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	2026-05-18T03:56:10.974191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bee11dd232d47ed2abb465bf1b942f59ff9bed88c6f698d2fc77fd07b6de0a4c

Aliases

arxiv: math/0601455 · arxiv_version: math/0601455v2 · doi: 10.48550/arxiv.math/0601455 · pith_short_12: X3QR3URS2R7N · pith_short_16: X3QR3URS2R7NFK5U · pith_short_8: X3QR3URS

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/X3QR3URS2R7NFK5UMW7RXFBPLH \
  | 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: bee11dd232d47ed2abb465bf1b942f59ff9bed88c6f698d2fc77fd07b6de0a4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31ebfa1c9686f7b3e6f0e8585df81f5d3299274132cb5c0e719e1ef5a84463d4",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2006-01-18T21:34:37Z",
    "title_canon_sha256": "7d37e208cd2a9b7ba93c63f0f5264150a5ca5a036a0f0968d7056758aefa9abe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601455",
    "kind": "arxiv",
    "version": 2
  }
}