Pith Number

pith:BBS4ZA5R

pith:2007:BBS4ZA5RMHNORGZRJ7PFBSA367

not attested not anchored not stored refs pending

Appendix to 'Roth's theorem on progressions revisited' by J Bourgain

Tom Sanders

arxiv:0710.0642 v4 · 2007-10-02 · math.CA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BBS4ZA5RMHNORGZRJ7PFBSA367}

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	2026-05-18T04:37:34.527505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0865cc83b161dae89b314fde50c81bf7d965220f6cb32c7f1d59ecfddbd1c136

Aliases

arxiv: 0710.0642 · arxiv_version: 0710.0642v4 · doi: 10.48550/arxiv.0710.0642 · pith_short_12: BBS4ZA5RMHNO · pith_short_16: BBS4ZA5RMHNORGZR · pith_short_8: BBS4ZA5R

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/BBS4ZA5RMHNORGZRJ7PFBSA367 \
  | 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: 0865cc83b161dae89b314fde50c81bf7d965220f6cb32c7f1d59ecfddbd1c136

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b42fb0ea85943e63590a124f74941b0ebac7445879ee5c03bbbbce9d949af033",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2007-10-02T20:41:24Z",
    "title_canon_sha256": "9369058d3844a21cc1fe97500eda433a98bc5b7db7f0d8e77dcb5bdacf5f25ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.0642",
    "kind": "arxiv",
    "version": 4
  }
}