Pith Number

pith:QRB2YT5O

pith:2024:QRB2YT5OOGLDXQDWUNOIIOHESC

not attested not anchored not stored refs pending

Random multiplicative functions and typical size of character in short intervals

Rachid Caich

arxiv:2402.06426 v1 · 2024-02-09 · 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{QRB2YT5OOGLDXQDWUNOIIOHESC}

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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.

Cited by

4 papers in Pith

Character sums over smooth numbers

Escaping Chaos in Random Multiplicative Functions

Distribution of random multiplicative functions in short intervals, with proper normalization

Escaping Chaos in Random Multiplicative Functions

Receipt and verification

First computed	2026-07-05T07:43:24.062560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8443ac4fae71963bc076a35c8438e490a5bbc344e67dc410191a2742347357d1

Aliases

arxiv: 2402.06426 · arxiv_version: 2402.06426v1 · doi: 10.48550/arxiv.2402.06426 · pith_short_12: QRB2YT5OOGLD · pith_short_16: QRB2YT5OOGLDXQDW · pith_short_8: QRB2YT5O

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/QRB2YT5OOGLDXQDWUNOIIOHESC \
  | 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: 8443ac4fae71963bc076a35c8438e490a5bbc344e67dc410191a2742347357d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9958ec116332ada28d1c499f43013086ccee7f8c521d64de56abfcb73f6905a3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-02-09T14:15:07Z",
    "title_canon_sha256": "84b7fa339b4d5dc833d1dbb4678aa9ea818f4ca3613bbead13bfb7ae02a89b1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.06426",
    "kind": "arxiv",
    "version": 1
  }
}