Pith Number

pith:PTEG4EOX

pith:2013:PTEG4EOX2QFFFX5A7G7LZCY7XO

not attested not anchored not stored refs pending

A Categorification of Hall Algebras

Christopher Walker

arxiv:1304.0219 v2 · 2013-03-31 · 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{PTEG4EOX2QFFFX5A7G7LZCY7XO}

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	2026-05-18T03:29:15.383349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cc86e11d7d40a52dfa0f9bebc8b1fbb80e05d0efb8185220419d39ddff09fb4

Aliases

arxiv: 1304.0219 · arxiv_version: 1304.0219v2 · doi: 10.48550/arxiv.1304.0219 · pith_short_12: PTEG4EOX2QFF · pith_short_16: PTEG4EOX2QFFFX5A · pith_short_8: PTEG4EOX

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/PTEG4EOX2QFFFX5A7G7LZCY7XO \
  | 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: 7cc86e11d7d40a52dfa0f9bebc8b1fbb80e05d0efb8185220419d39ddff09fb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee5e059d7e9126292643115952dd5409ff8cd1d8d6525ecbe9cb100959aaacb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2013-03-31T15:47:19Z",
    "title_canon_sha256": "0e5fb2fa8e1d0290ae3f5b9407ad0532b4c48ecc523b352ae571fcba7c8d1968"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0219",
    "kind": "arxiv",
    "version": 2
  }
}