Pith Number

pith:XYZW2RKN

pith:2015:XYZW2RKNQD6IACFQTPZXEXMQRA

not attested not anchored not stored refs pending

Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals

El Houcein El Abdalaoui (LMRS), Mariusz Lemanczyk, Thierry de la Rue (LMRS)

arxiv:1507.04132 v1 · 2015-07-15 · 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{XYZW2RKNQD6IACFQTPZXEXMQRA}

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	2026-05-18T01:36:49.052419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be336d454d80fc8008b09bf3725d90880ab44d76e978ffacdeac1a7664604e92

Aliases

arxiv: 1507.04132 · arxiv_version: 1507.04132v1 · doi: 10.48550/arxiv.1507.04132 · pith_short_12: XYZW2RKNQD6I · pith_short_16: XYZW2RKNQD6IACFQ · pith_short_8: XYZW2RKN

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/XYZW2RKNQD6IACFQTPZXEXMQRA \
  | 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: be336d454d80fc8008b09bf3725d90880ab44d76e978ffacdeac1a7664604e92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed85fea620249653fb4345051e6861fa1286e7c77d74541c2b5d434b4f5d2f6e",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-07-15T09:04:37Z",
    "title_canon_sha256": "c275bf6c9b92a945114bae1585c0801d1228a2e81a570d4c7bc62a8c60d93a2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04132",
    "kind": "arxiv",
    "version": 1
  }
}