Pith Number

pith:COS77S6V

pith:2016:COS77S6VRAABHYBXBA7Z6VSNSB

not attested not anchored not stored refs pending

On Asymptotic Approximate Groups of Integers

Bela Bajnok

arxiv:1603.06553 v1 · 2016-03-21 · 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{COS77S6VRAABHYBXBA7Z6VSNSB}

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	2026-05-18T01:18:48.293677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13a5ffcbd5880013e037083f9f564d90686bd39bc34d6e9a7addffd7d54081eb

Aliases

arxiv: 1603.06553 · arxiv_version: 1603.06553v1 · doi: 10.48550/arxiv.1603.06553 · pith_short_12: COS77S6VRAAB · pith_short_16: COS77S6VRAABHYBX · pith_short_8: COS77S6V

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/COS77S6VRAABHYBXBA7Z6VSNSB \
  | 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: 13a5ffcbd5880013e037083f9f564d90686bd39bc34d6e9a7addffd7d54081eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf1ad54eecb85769ac8ce969eb9d85c8c4c4b56fc91834210050b4e383fd328d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-21T19:37:20Z",
    "title_canon_sha256": "60159bef8d0860155b41ec6dbcca379ee91bb7bdc3d7547dab785f6982624385"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06553",
    "kind": "arxiv",
    "version": 1
  }
}