Pith Number

pith:VJ7TW6DY

pith:2015:VJ7TW6DYOYP4JBVXQUTQYAPRT4

not attested not anchored not stored refs pending

Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences, II

Clemens M\"ullner, Lukas Spiegelhofer

arxiv:1511.01671 v2 · 2015-11-05 · 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{VJ7TW6DYOYP4JBVXQUTQYAPRT4}

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	2026-05-18T00:30:33.168128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa7f3b7878761fc486b785270c01f19f03c4cf61c9e154580058927b5b0d75de

Aliases

arxiv: 1511.01671 · arxiv_version: 1511.01671v2 · doi: 10.48550/arxiv.1511.01671 · pith_short_12: VJ7TW6DYOYP4 · pith_short_16: VJ7TW6DYOYP4JBVX · pith_short_8: VJ7TW6DY

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/VJ7TW6DYOYP4JBVXQUTQYAPRT4 \
  | 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: aa7f3b7878761fc486b785270c01f19f03c4cf61c9e154580058927b5b0d75de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e9cd3d0578728f74ff741dcd401442947977cdca540280ea6d92e698cb7543",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-11-05T09:38:19Z",
    "title_canon_sha256": "3b0fba9dd3e3428260073f2bf77f35724ebb9ac5367609d74d455e578f0d6af6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01671",
    "kind": "arxiv",
    "version": 2
  }
}