Pith Number

pith:M7GPIL4T

pith:2022:M7GPIL4T7V2VAJU6CUCVYFGZJF

not attested not anchored not stored refs pending

The Distribution of Error Terms of Smoothed Summatory Totient Functions

Hamilton Wan, Hannah Lang, Nancy Xu, Sanjana Das

arxiv:2207.07722 v1 · 2022-07-15 · 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{M7GPIL4T7V2VAJU6CUCVYFGZJF}

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	2026-07-05T04:40:36.311864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67ccf42f93fd7550269e15055c14d94963b0216d8ec964fa00465fef9cd09895

Aliases

arxiv: 2207.07722 · arxiv_version: 2207.07722v1 · doi: 10.48550/arxiv.2207.07722 · pith_short_12: M7GPIL4T7V2V · pith_short_16: M7GPIL4T7V2VAJU6 · pith_short_8: M7GPIL4T

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/M7GPIL4T7V2VAJU6CUCVYFGZJF \
  | 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: 67ccf42f93fd7550269e15055c14d94963b0216d8ec964fa00465fef9cd09895

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d189d4162263661f4b51d5a19ec2eccdb68bd3428ade860babe6164425e5e7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-07-15T19:29:04Z",
    "title_canon_sha256": "2407e50cb11d6f4cb21cb4ae63b6bf30f89ab78411645d0035f86ef7fd9ad238"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.07722",
    "kind": "arxiv",
    "version": 1
  }
}