Pith Number

pith:J7OMYCFE

pith:2016:J7OMYCFESGCZBUP4NAD4ZLQHZK

not attested not anchored not stored refs pending

Gowers norms of multiplicative functions in progressions on average

Xuancheng Shao

arxiv:1607.01814 v2 · 2016-07-06 · 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{J7OMYCFESGCZBUP4NAD4ZLQHZK}

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	2026-05-18T00:41:26.123803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fdccc08a4918590d1fc6807ccae07ca9fa8ec487e82ea8d029a898b4cadbf4d

Aliases

arxiv: 1607.01814 · arxiv_version: 1607.01814v2 · doi: 10.48550/arxiv.1607.01814 · pith_short_12: J7OMYCFESGCZ · pith_short_16: J7OMYCFESGCZBUP4 · pith_short_8: J7OMYCFE

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/J7OMYCFESGCZBUP4NAD4ZLQHZK \
  | 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: 4fdccc08a4918590d1fc6807ccae07ca9fa8ec487e82ea8d029a898b4cadbf4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9aec947c4481bb3ac47641b46fa27eddbe576304197b4fe320fc87062bef0301",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-07-06T21:17:02Z",
    "title_canon_sha256": "0bd1553dcb32f1956ad6d7cc45577ab666f655b9b318574775ec6a82d78801d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01814",
    "kind": "arxiv",
    "version": 2
  }
}