Pith Number

pith:AKPMSZOM

pith:2007:AKPMSZOMK4S6IMN2URBRFA4VGW

not attested not anchored not stored refs pending

Irrationality measure and lower bounds for pi(x)

Ben Wieland, David Burt, Matthew Schiffman, Sam Donow, Steven J. Miller

arxiv:0709.2184 v4 · 2007-09-13 · 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{AKPMSZOMK4S6IMN2URBRFA4VGW}

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	2026-05-18T02:30:41.010734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

029ec965cc5725e431baa44312839535937495be33d6e45c63c5d27c4e516760

Aliases

arxiv: 0709.2184 · arxiv_version: 0709.2184v4 · doi: 10.48550/arxiv.0709.2184 · pith_short_12: AKPMSZOMK4S6 · pith_short_16: AKPMSZOMK4S6IMN2 · pith_short_8: AKPMSZOM

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/AKPMSZOMK4S6IMN2URBRFA4VGW \
  | 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: 029ec965cc5725e431baa44312839535937495be33d6e45c63c5d27c4e516760

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c24c8cc37cc30325f5c54a0bf2bc372717430ba1506c38a4fccf4f5614a07ede",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-13T23:02:15Z",
    "title_canon_sha256": "0daf668bee5a4ad2d154ccae2dae88bf2bf69b36d1b962c4420bf5ceee3cae1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2184",
    "kind": "arxiv",
    "version": 4
  }
}