Pith Number

pith:ATFQCFBW

pith:2008:ATFQCFBW42O7LRA3ICLW24RGLP

not attested not anchored not stored refs pending

The Mobius function is strongly orthogonal to nilsequences

Ben Green, Terence Tao

arxiv:0807.1736 v4 · 2008-07-10 · 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{ATFQCFBW42O7LRA3ICLW24RGLP}

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.

Cited by

1 paper in Pith

M\"obius randomness in the Hartle-Hawking state

Receipt and verification

First computed	2026-05-18T03:24:42.869055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04cb011436e69df5c41b40976d72265bd71f065504bbf5805e85fd6e65d46117

Aliases

arxiv: 0807.1736 · arxiv_version: 0807.1736v4 · doi: 10.48550/arxiv.0807.1736 · pith_short_12: ATFQCFBW42O7 · pith_short_16: ATFQCFBW42O7LRA3 · pith_short_8: ATFQCFBW

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/ATFQCFBW42O7LRA3ICLW24RGLP \
  | 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: 04cb011436e69df5c41b40976d72265bd71f065504bbf5805e85fd6e65d46117

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "722a09b047cf287da36a2af0d4770f529ef35db2159440dbf7ce1a830089d22f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-07-10T20:39:38Z",
    "title_canon_sha256": "357a28be53355595641a370b7986246b3977199a20f21c6fa4df4c8b00036f64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.1736",
    "kind": "arxiv",
    "version": 4
  }
}