Pith Number

pith:Y7I5IA64

pith:2018:Y7I5IA64W3YLQHQMMYVINSWAQP

not attested not anchored not stored refs pending

On the number of $k$th powers inside arithmetic progressions

Ciprian Demeter, Jean Bourgain

arxiv:1811.11919 v2 · 2018-11-29 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y7I5IA64W3YLQHQMMYVINSWAQP}

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	2026-05-17T23:58:47.160256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7d1d403dcb6f0b81e0c662a86cac083e4be4f3528dfdd85980ac68f3bd5a99e

Aliases

arxiv: 1811.11919 · arxiv_version: 1811.11919v2 · doi: 10.48550/arxiv.1811.11919 · pith_short_12: Y7I5IA64W3YL · pith_short_16: Y7I5IA64W3YLQHQM · pith_short_8: Y7I5IA64

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/Y7I5IA64W3YLQHQMMYVINSWAQP \
  | 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: c7d1d403dcb6f0b81e0c662a86cac083e4be4f3528dfdd85980ac68f3bd5a99e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "438cdb5b196cd9673bcf0c8e036cfd7381801f680827eaec44acd447df4b0e24",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-29T02:01:20Z",
    "title_canon_sha256": "4a91041962818cbf990e33a1b4759201d40a69ead6c90bb7e4b29fe8751ff61c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.11919",
    "kind": "arxiv",
    "version": 2
  }
}