Pith Number

pith:ACX3AECY

pith:2026:ACX3AECYTWYXN4JT2ZT4L6JE23

not attested not anchored not stored refs pending

Rank Amplification for Shifted Equal Values of Euler's Totient Function

Eric Li (Trinity College, University of Cambridge)

arxiv:2606.23681 v1 · 2026-06-22 · 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{ACX3AECYTWYXN4JT2ZT4L6JE23}

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	2026-06-23T03:14:34.546538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00afb010589db176f133d667c5f924d6e326d1dabafd70f3e6688c1a85d71100

Aliases

arxiv: 2606.23681 · arxiv_version: 2606.23681v1 · doi: 10.48550/arxiv.2606.23681 · pith_short_12: ACX3AECYTWYX · pith_short_16: ACX3AECYTWYXN4JT · pith_short_8: ACX3AECY

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/ACX3AECYTWYXN4JT2ZT4L6JE23 \
  | 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: 00afb010589db176f133d667c5f924d6e326d1dabafd70f3e6688c1a85d71100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "554250a8cd80955ab88f060b8e7a0db7b15fa71592a07a4d7c22d853bfe9c3c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-22T17:59:25Z",
    "title_canon_sha256": "7d6b05089ea801f43c905f63c1ef1b3bf245bea0eb7c6769fd215cea8beba464"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23681",
    "kind": "arxiv",
    "version": 1
  }
}