Pith Number

pith:7ESAQACR

pith:2026:7ESAQACRR7U3YGLGX2TGD7NM5G

not attested not anchored not stored refs pending

Explicit Factorization of $X^n-1$ over $\mathbb{Z}_{p^e}$ via Cofactor-Free Single-Seed Hensel Lifting

Jiansheng Yang, Yang Ding, Yongchao Wang, Zhiqiu Huang

arxiv:2606.20633 v1 · 2026-05-30 · cs.SC · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ESAQACRR7U3YGLGX2TGD7NM5G}

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	2026-06-23T00:11:52.058782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9240800518fe9bc1966bea661fdace98d9ecc3100cf3254a3f274093448824c

Aliases

arxiv: 2606.20633 · arxiv_version: 2606.20633v1 · doi: 10.48550/arxiv.2606.20633 · pith_short_12: 7ESAQACRR7U3 · pith_short_16: 7ESAQACRR7U3YGLG · pith_short_8: 7ESAQACR

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/7ESAQACRR7U3YGLGX2TGD7NM5G \
  | 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: f9240800518fe9bc1966bea661fdace98d9ecc3100cf3254a3f274093448824c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44ad5721f1d2cb8d24915554174cff5e5dad6b3e349bee0bfa449e37e2a194dc",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2026-05-30T07:55:32Z",
    "title_canon_sha256": "66326be343b4e19a86030917616931bb22b6c0479bd2ad8433cafbf4601ea80c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20633",
    "kind": "arxiv",
    "version": 1
  }
}