Pith Number

pith:M43TCWDV

pith:2026:M43TCWDVJE5GPA7IB5EIMK45B3

not attested not anchored not stored refs pending

Extended heart construction (I): The heart of $n$-cotorsion pairs on triangulated categories

Hiroyuki Nakaoka, Nao Mochizuki, Yasuaki Ogawa

arxiv:2608.03212 v1 · 2026-08-04 · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M43TCWDVJE5GPA7IB5EIMK45B3}

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	2026-08-05T00:46:17.197860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6737315875493a6783e80f48862b9d0ec5a9a4832857f0edc183b8b85da24643

Aliases

arxiv: 2608.03212 · arxiv_version: 2608.03212v1 · doi: 10.48550/arxiv.2608.03212 · pith_short_12: M43TCWDVJE5G · pith_short_16: M43TCWDVJE5GPA7I · pith_short_8: M43TCWDV

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/M43TCWDVJE5GPA7IB5EIMK45B3 \
  | 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: 6737315875493a6783e80f48862b9d0ec5a9a4832857f0edc183b8b85da24643

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea47afa19e8754ec0adf4c96b74325eb21efb6df216a559881c293792664fafe",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-08-04T06:49:45Z",
    "title_canon_sha256": "08dee1d815bce5ac3c0ce6505445fbba6317664b81340dbca1bbead20e7718d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03212",
    "kind": "arxiv",
    "version": 1
  }
}