Pith Number

pith:X5WHKWFB

pith:2016:X5WHKWFBLYZ2JUI6JCAT2BGDPD

not attested not anchored not stored refs pending

On Representation of Integers from Thin Subgroups of SL(2,Z) with Parabolics

Xin Zhang

arxiv:1610.00770 v3 · 2016-10-03 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X5WHKWFBLYZ2JUI6JCAT2BGDPD}

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	2026-05-18T00:12:00.850680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf6c7558a15e33a4d11e48813d04c378ec31229c485272a2aff1690a7af90d41

Aliases

arxiv: 1610.00770 · arxiv_version: 1610.00770v3 · doi: 10.48550/arxiv.1610.00770 · pith_short_12: X5WHKWFBLYZ2 · pith_short_16: X5WHKWFBLYZ2JUI6 · pith_short_8: X5WHKWFB

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/X5WHKWFBLYZ2JUI6JCAT2BGDPD \
  | 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: bf6c7558a15e33a4d11e48813d04c378ec31229c485272a2aff1690a7af90d41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c87eb8f5f62c3ef194a9cb4ecf7bb9555aa19f0c2c8ce4281291d4b163251c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-03T22:05:48Z",
    "title_canon_sha256": "398bad9ba719fc6de44e7c090145cde1440dc25467073d025e4f886448c40a5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.00770",
    "kind": "arxiv",
    "version": 3
  }
}