Pith Number

pith:I7YG3QB7

pith:2012:I7YG3QB7M63TWBDRC3MBOGQYRT

not attested not anchored not stored refs pending

Nonstandard Analysis and the sumset phenomenon in arbitrary amenable groups

Martino Lupini, Mauro Di Nasso

arxiv:1211.4208 v2 · 2012-11-18 · 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{I7YG3QB7M63TWBDRC3MBOGQYRT}

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	2026-05-18T01:15:36.662304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47f06dc03f67b73b047116d8171a188ce575cf01b4284b2d7c70da7fbea100a0

Aliases

arxiv: 1211.4208 · arxiv_version: 1211.4208v2 · doi: 10.48550/arxiv.1211.4208 · pith_short_12: I7YG3QB7M63T · pith_short_16: I7YG3QB7M63TWBDR · pith_short_8: I7YG3QB7

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/I7YG3QB7M63TWBDRC3MBOGQYRT \
  | 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: 47f06dc03f67b73b047116d8171a188ce575cf01b4284b2d7c70da7fbea100a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "521d07bcdd0d69f083a40503936578b89c651924c1c37bf8e60fce3ab29ee9e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-18T11:13:25Z",
    "title_canon_sha256": "89f177d370f93dc006fae4e72b66b9311e1144d9968a7defd2b3e8648c69bf1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4208",
    "kind": "arxiv",
    "version": 2
  }
}