Pith Number

pith:DM63T7YJ

pith:2016:DM63T7YJJHCZTSM5YT54YHIA23

not attested not anchored not stored refs pending

Progression-free sets in Z_4^n are exponentially small

Ernie Croot, Peter Pach, Vsevolod Lev

arxiv:1605.01506 v2 · 2016-05-05 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DM63T7YJJHCZTSM5YT54YHIA23}

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	2026-05-18T01:14:12.182892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b3db9ff0949c599c99dc4fbcc1d00d6dd854bfcc643eaab43e3897e454cb465

Aliases

arxiv: 1605.01506 · arxiv_version: 1605.01506v2 · doi: 10.48550/arxiv.1605.01506 · pith_short_12: DM63T7YJJHCZ · pith_short_16: DM63T7YJJHCZTSM5 · pith_short_8: DM63T7YJ

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/DM63T7YJJHCZTSM5YT54YHIA23 \
  | 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: 1b3db9ff0949c599c99dc4fbcc1d00d6dd854bfcc643eaab43e3897e454cb465

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8ba5e7232d6d9d42df92b795aa52f7a24633d827ba4ba8e03863544f18ba896",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-05-05T07:03:29Z",
    "title_canon_sha256": "1eb740a0e452748f7ffaf9597e9336ad67e52c94af139758dcbd61e4eb19c0db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.01506",
    "kind": "arxiv",
    "version": 2
  }
}