Pith Number

pith:HH77HR3L

pith:2012:HH77HR3L2JRPVCYFVFN4FIS27W

not attested not anchored not stored refs pending

Density of integral sets with missing differences

Min Tang, Quan-Hui Yang

arxiv:1212.0209 v2 · 2012-12-02 · 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{HH77HR3L2JRPVCYFVFN4FIS27W}

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	2026-05-18T03:14:50.148296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39fff3c76bd262fa8b05a95bc2a25afdb7ddfadd581e66972302bf4858a7e577

Aliases

arxiv: 1212.0209 · arxiv_version: 1212.0209v2 · doi: 10.48550/arxiv.1212.0209 · pith_short_12: HH77HR3L2JRP · pith_short_16: HH77HR3L2JRPVCYF · pith_short_8: HH77HR3L

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/HH77HR3L2JRPVCYFVFN4FIS27W \
  | 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: 39fff3c76bd262fa8b05a95bc2a25afdb7ddfadd581e66972302bf4858a7e577

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9dc83e2241bbec8bb5124957cce1061ce0007fd40c1e184391a59895e34557dd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-02T13:59:21Z",
    "title_canon_sha256": "5798130d5c3033b064e3ce231214915170459a2e04c1254f2f845d3056b137e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0209",
    "kind": "arxiv",
    "version": 2
  }
}