Pith Number

pith:QGCEU6XF

pith:2010:QGCEU6XFNSTJFRLUWY4HL3DN2Z

not attested not anchored not stored refs pending

On the structure of ($-\beta$)-integers

Wolfgang Steiner (LIAFA)

arxiv:1011.1755 v2 · 2010-11-08 · math.NT · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QGCEU6XFNSTJFRLUWY4HL3DN2Z}

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	2026-05-18T03:59:36.930516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81844a7ae56ca692c574b63875ec6dd640ae46058d7dc1f3b3804eb5796e7d3f

Aliases

arxiv: 1011.1755 · arxiv_version: 1011.1755v2 · doi: 10.48550/arxiv.1011.1755 · pith_short_12: QGCEU6XFNSTJ · pith_short_16: QGCEU6XFNSTJFRLU · pith_short_8: QGCEU6XF

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/QGCEU6XFNSTJFRLUWY4HL3DN2Z \
  | 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: 81844a7ae56ca692c574b63875ec6dd640ae46058d7dc1f3b3804eb5796e7d3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1956526832575f2c7973ef8eaa82c95c66140437a22c5758a817cb307a0e28e",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-11-08T10:25:06Z",
    "title_canon_sha256": "99484698e7f21e9a95dec2a0b8f2937fd0ca0136807216e993da84b4a54f074d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1755",
    "kind": "arxiv",
    "version": 2
  }
}