Pith Number

pith:TTJVNLBX

pith:2014:TTJVNLBX5QP74KH6J35SB4RTMX

not attested not anchored not stored refs pending

Upper and lower fast Khintchine spectra in continued fractions

Lingmin Liao (LAMA), Michal Rams (PAN)

arxiv:1406.1148 v2 · 2014-06-04 · math.DS · 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{TTJVNLBX5QP74KH6J35SB4RTMX}

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	2026-05-18T01:28:35.210383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cd356ac37ec1ffe28fe4efb20f23365f55ec0c7db7f92677bf9a1b430864a0e

Aliases

arxiv: 1406.1148 · arxiv_version: 1406.1148v2 · doi: 10.48550/arxiv.1406.1148 · pith_short_12: TTJVNLBX5QP7 · pith_short_16: TTJVNLBX5QP74KH6 · pith_short_8: TTJVNLBX

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/TTJVNLBX5QP74KH6J35SB4RTMX \
  | 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: 9cd356ac37ec1ffe28fe4efb20f23365f55ec0c7db7f92677bf9a1b430864a0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86680fd6213a676ea3a3c4d9ca6f8420fb65b15d94e799e14f9ff7baf0499694",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-06-04T19:06:38Z",
    "title_canon_sha256": "c227127a50e27bbc880c71d54d8cbac92a1eedb22ddbbb43a45a4f54a78dd124"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.1148",
    "kind": "arxiv",
    "version": 2
  }
}