Pith Number

pith:MMOHKEKS

pith:2013:MMOHKEKSDLQ2LYHPAKFREBK6QV

not attested not anchored not stored refs pending

On the upper semi-continuity of HSL numbers

Serena Murru

arxiv:1302.1124 v3 · 2013-02-05 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MMOHKEKSDLQ2LYHPAKFREBK6QV}

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.

Cited by

1 paper in Pith

A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings

Receipt and verification

First computed	2026-05-18T01:15:59.401154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

631c7511521ae1a5e0ef028b12055e857a883c125082ed662f79541ba1ef0705

Aliases

arxiv: 1302.1124 · arxiv_version: 1302.1124v3 · doi: 10.48550/arxiv.1302.1124 · pith_short_12: MMOHKEKSDLQ2 · pith_short_16: MMOHKEKSDLQ2LYHP · pith_short_8: MMOHKEKS

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/MMOHKEKSDLQ2LYHPAKFREBK6QV \
  | 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: 631c7511521ae1a5e0ef028b12055e857a883c125082ed662f79541ba1ef0705

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8edfd6efc9d95e7750cf0edf79f8f666571d322e92401c3d10741eccc0b13074",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-02-05T17:11:37Z",
    "title_canon_sha256": "501063e644984bb18e8715bc2655b7d1ea82101a7ca5d5725759b1328841ac5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.1124",
    "kind": "arxiv",
    "version": 3
  }
}