Pith Number

pith:4RP5VWE3

pith:2012:4RP5VWE3EHQLLOAVK5YDBTSTD4

not attested not anchored not stored refs pending

Remarks on Hall algebras of triangulated categories

Fan Xu, Jie Xiao

arxiv:1208.2312 v2 · 2012-08-11 · 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{4RP5VWE3EHQLLOAVK5YDBTSTD4}

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	2026-05-18T01:28:21.626882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e45fdad89b21e0b5b815577030ce531f1ae7fe7ba95d1e4cc92d9916589890b0

Aliases

arxiv: 1208.2312 · arxiv_version: 1208.2312v2 · doi: 10.48550/arxiv.1208.2312 · pith_short_12: 4RP5VWE3EHQL · pith_short_16: 4RP5VWE3EHQLLOAV · pith_short_8: 4RP5VWE3

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/4RP5VWE3EHQLLOAVK5YDBTSTD4 \
  | 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: e45fdad89b21e0b5b815577030ce531f1ae7fe7ba95d1e4cc92d9916589890b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61705c01f89b990af5cd99bd0aa4db8395b90f9bb6c29655228e554d1333350f",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-08-11T06:40:47Z",
    "title_canon_sha256": "bc5c591feb92a6db119999b9166b2c45f107a16455a25ab2fb3a8413a7c9b2fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2312",
    "kind": "arxiv",
    "version": 2
  }
}