Pith Number

pith:773CIIY6

pith:2013:773CIIY6CX2HJ3QQGLBJXSOUMR

not attested not anchored not stored refs pending

High density piecewise syndeticity of sumsets

Isaac Goldbring, Karl Mahlburg, Martino Lupini, Mauro Di Nasso, Renling Jin, Steven Leth

arxiv:1310.5729 v2 · 2013-10-21 · math.NT · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{773CIIY6CX2HJ3QQGLBJXSOUMR}

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	2026-05-18T00:38:31.653429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fff624231e15f474ee1032c29bc9d464589e83570784ce5aeac1ab6268f26594

Aliases

arxiv: 1310.5729 · arxiv_version: 1310.5729v2 · doi: 10.48550/arxiv.1310.5729 · pith_short_12: 773CIIY6CX2H · pith_short_16: 773CIIY6CX2HJ3QQ · pith_short_8: 773CIIY6

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/773CIIY6CX2HJ3QQGLBJXSOUMR \
  | 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: fff624231e15f474ee1032c29bc9d464589e83570784ce5aeac1ab6268f26594

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ebc5fc277726500546ce6e662f9635b5e0a768ce284db489f049acc92e9e8bf",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-10-21T21:14:03Z",
    "title_canon_sha256": "0e6bc8bc9a555a93c1073deeb0e905ef14ed16aeb746e87f624537f824cf70ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.5729",
    "kind": "arxiv",
    "version": 2
  }
}