Pith Number

pith:HABVMSX7

pith:2015:HABVMSX77OXRJM6XPI7WYUGI5I

not attested not anchored not stored refs pending

Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$

Shenxing Zhang, Yi Ouyang

arxiv:1511.00084 v1 · 2015-10-31 · 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{HABVMSX77OXRJM6XPI7WYUGI5I}

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	2026-05-18T01:28:13.402096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3803564afffbaf14b3d77a3f6c50c8ea23af67b72aed185675da2d34f337f832

Aliases

arxiv: 1511.00084 · arxiv_version: 1511.00084v1 · doi: 10.48550/arxiv.1511.00084 · pith_short_12: HABVMSX77OXR · pith_short_16: HABVMSX77OXRJM6X · pith_short_8: HABVMSX7

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/HABVMSX77OXRJM6XPI7WYUGI5I \
  | 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: 3803564afffbaf14b3d77a3f6c50c8ea23af67b72aed185675da2d34f337f832

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8927e7044d25d856cbc2c2e956d99e7970b8b927c5cbb332c62ae9497d654ae1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-31T06:15:55Z",
    "title_canon_sha256": "e543bd4763832c392f25e1cd1948e26583329ebcb06f13b98a42cec6c4c7b0dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00084",
    "kind": "arxiv",
    "version": 1
  }
}