Pith Number

pith:Y4ANWFKI

pith:2016:Y4ANWFKIXFQU5VLX3OU3RKU5CO

not attested not anchored not stored refs pending

On Doubling and Volume: Chains

G. A. Freiman, O. Serra

arxiv:1608.04916 v2 · 2016-08-17 · 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{Y4ANWFKIXFQU5VLX3OU3RKU5CO}

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	2026-05-18T00:52:44.146440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c700db1548b9614ed577dba9b8aa9d139e7c6c486af910275011db600999e988

Aliases

arxiv: 1608.04916 · arxiv_version: 1608.04916v2 · doi: 10.48550/arxiv.1608.04916 · pith_short_12: Y4ANWFKIXFQU · pith_short_16: Y4ANWFKIXFQU5VLX · pith_short_8: Y4ANWFKI

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/Y4ANWFKIXFQU5VLX3OU3RKU5CO \
  | 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: c700db1548b9614ed577dba9b8aa9d139e7c6c486af910275011db600999e988

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b20e7d9aec46327fd632c0a0a5c71c1b2b8e6a67181dabe64abf90551ffd852",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-17T10:07:35Z",
    "title_canon_sha256": "f86fad794f0d522d18962280b676b6e96acc8cf2e8ef245eccea6b827046c030"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04916",
    "kind": "arxiv",
    "version": 2
  }
}