Pith Number

pith:G4RST3NO

pith:2016:G4RST3NOONKL5NB6Z7EXPAEXL6

not attested not anchored not stored refs pending

Lower bounds for the variance of sequences in arithmetic progressions: primes and divisor functions

Adam J. Harper, Kannan Soundararajan

arxiv:1602.01984 v1 · 2016-02-05 · 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{G4RST3NOONKL5NB6Z7EXPAEXL6}

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	2026-05-18T01:21:14.862188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

372329edae7354beb43ecfc97780975fb4c1ff05117628a2f2394b2684bb9cbc

Aliases

arxiv: 1602.01984 · arxiv_version: 1602.01984v1 · doi: 10.48550/arxiv.1602.01984 · pith_short_12: G4RST3NOONKL · pith_short_16: G4RST3NOONKL5NB6 · pith_short_8: G4RST3NO

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/G4RST3NOONKL5NB6Z7EXPAEXL6 \
  | 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: 372329edae7354beb43ecfc97780975fb4c1ff05117628a2f2394b2684bb9cbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e89ab1a329cb2ddbab15586481b31badb2c56c29f888efb53a4e64e094ac6e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-02-05T11:38:28Z",
    "title_canon_sha256": "88b1c497aeef2e2e5ed0d27e2ead9f99cc5408e210b248c4276aa1635174d55f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01984",
    "kind": "arxiv",
    "version": 1
  }
}