Pith Number

pith:ZNMSW2EI

pith:2016:ZNMSW2EIM555Q5I2U6W7I4RJ4O

not attested not anchored not stored refs pending

Extremal product-one free sequences in $C_q \rtimes_s C_m$

Fabio Enrique Brochero Mart\'inez, S\'avio Ribas

arxiv:1610.09870 v1 · 2016-10-31 · 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{ZNMSW2EIM555Q5I2U6W7I4RJ4O}

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	2026-05-18T00:51:42.769614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb592b6888677bd8751aa7adf47229e3806104f395e5995637d7d400a57942aa

Aliases

arxiv: 1610.09870 · arxiv_version: 1610.09870v1 · doi: 10.48550/arxiv.1610.09870 · pith_short_12: ZNMSW2EIM555 · pith_short_16: ZNMSW2EIM555Q5I2 · pith_short_8: ZNMSW2EI

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/ZNMSW2EIM555Q5I2U6W7I4RJ4O \
  | 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: cb592b6888677bd8751aa7adf47229e3806104f395e5995637d7d400a57942aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1d2e5bd0023cea7fe1a13844687221e42026d88021404d5964c2aca4fa3f9db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-31T11:20:16Z",
    "title_canon_sha256": "943ceb77155853cd29f05044b43c711979271700b89ce8d6c30fd81fc067ac2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.09870",
    "kind": "arxiv",
    "version": 1
  }
}