Pith Number

pith:IZ2N2JCI

pith:2006:IZ2N2JCICFJBYVXYAJ27HYTTQU

not attested not anchored not stored refs pending

Hall algebras associated to triangulated categories

Fan Xu, Jie Xiao

arxiv:math/0608144 v4 · 2006-08-06 · math.QA · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IZ2N2JCICFJBYVXYAJ27HYTTQU}

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

2 papers in Pith

Hall Geometry and Auslander-Reiten Quiver

Receipt and verification

First computed	2026-07-04T15:13:51.684797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4674dd244811521c56f80275f3e2738531d459db31bd042e9d194980933bb2de

Aliases

arxiv: math/0608144 · arxiv_version: math/0608144v4 · doi: 10.48550/arxiv.math/0608144 · pith_short_12: IZ2N2JCICFJB · pith_short_16: IZ2N2JCICFJBYVXY · pith_short_8: IZ2N2JCI

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/IZ2N2JCICFJBYVXYAJ27HYTTQU \
  | 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: 4674dd244811521c56f80275f3e2738531d459db31bd042e9d194980933bb2de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d70a1d225eeaef3e789655abb638eb49297bc0664fea5aeda089aef0806bf09",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2006-08-06T11:27:33Z",
    "title_canon_sha256": "a4600093505a3dc70e829e43eeaef1bc50d08b49ab94173e9395c47984b09df4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608144",
    "kind": "arxiv",
    "version": 4
  }
}