Pith Number

pith:U573XRZ5

pith:2013:U573XRZ5O2IMXOGBHE4CD6JQI7

not attested not anchored not stored refs pending

The Affine Sieve Beyond Expansion I: Thin Hypotenuses

Alex Kontorovich, Jean Bourgain

arxiv:1307.3535 v1 · 2013-07-12 · 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{U573XRZ5O2IMXOGBHE4CD6JQI7}

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	2026-05-18T03:18:38.957729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a77fbbc73d7690cbb8c1393821f93047e0b20e38bb4aab15d749125424d69f47

Aliases

arxiv: 1307.3535 · arxiv_version: 1307.3535v1 · doi: 10.48550/arxiv.1307.3535 · pith_short_12: U573XRZ5O2IM · pith_short_16: U573XRZ5O2IMXOGB · pith_short_8: U573XRZ5

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/U573XRZ5O2IMXOGBHE4CD6JQI7 \
  | 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: a77fbbc73d7690cbb8c1393821f93047e0b20e38bb4aab15d749125424d69f47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1c6b7f3cc87ff828cef556e72a6df4068ac5c699d891d780189dbc8affb2d94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-07-12T18:27:44Z",
    "title_canon_sha256": "9a717940b906ee75f03ad2347abf4b685851ba67c439751521ec75239ccab94b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3535",
    "kind": "arxiv",
    "version": 1
  }
}