Pith Number

pith:SH2BNR5M

pith:2016:SH2BNR5MLOD5FYMADVQW4TN4A6

not attested not anchored not stored refs pending

A zero-one Law for improvements to Dirichlet's Theorem

Dmitry Kleinbock, Nick Wadleigh

arxiv:1609.06780 v3 · 2016-09-21 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SH2BNR5MLOD5FYMADVQW4TN4A6}

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	2026-05-18T00:50:30.896000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91f416c7ac5b87d2e1801d616e4dbc07bed8d2cca6e7fe5dd80fe1fa4156dc6b

Aliases

arxiv: 1609.06780 · arxiv_version: 1609.06780v3 · doi: 10.48550/arxiv.1609.06780 · pith_short_12: SH2BNR5MLOD5 · pith_short_16: SH2BNR5MLOD5FYMA · pith_short_8: SH2BNR5M

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/SH2BNR5MLOD5FYMADVQW4TN4A6 \
  | 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: 91f416c7ac5b87d2e1801d616e4dbc07bed8d2cca6e7fe5dd80fe1fa4156dc6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7df369c363c280203f096e1b2f372537d252998925fd876afa61b23440d277d",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-21T23:57:16Z",
    "title_canon_sha256": "5478a173feb0353de7725f6e036f9f3091c54988fdbe3abd844ab200d7c9d4f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06780",
    "kind": "arxiv",
    "version": 3
  }
}