Pith Number

pith:6SNG6QGT

pith:2011:6SNG6QGT4LD2QUKMDWHAAHR46J

not attested not anchored not stored refs pending

Substitutions and 1/2-Discrepancy of $\{n \theta + x\}$ \rm{II}

David Ralston

arxiv:1105.6301 v1 · 2011-05-31 · 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{6SNG6QGT4LD2QUKMDWHAAHR46J}

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	2026-05-18T04:20:59.781191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f49a6f40d3e2c7a8514c1d8e001e3cf27f398dfbd28bdc048a5d6e198ed7404e

Aliases

arxiv: 1105.6301 · arxiv_version: 1105.6301v1 · doi: 10.48550/arxiv.1105.6301 · pith_short_12: 6SNG6QGT4LD2 · pith_short_16: 6SNG6QGT4LD2QUKM · pith_short_8: 6SNG6QGT

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/6SNG6QGT4LD2QUKMDWHAAHR46J \
  | 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: f49a6f40d3e2c7a8514c1d8e001e3cf27f398dfbd28bdc048a5d6e198ed7404e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6974e6ed06a17adedf1237bc07efc272f09204feb676a04024b496a82dce157d",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-31T14:34:17Z",
    "title_canon_sha256": "2c66925c5506ec737d68cc38dcd1444242c03e65c73a95feda38f9ff9d40c5b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.6301",
    "kind": "arxiv",
    "version": 1
  }
}