Pith Number

pith:HA6UAW37

pith:2019:HA6UAW375RY7RX5UKKIAK44UHK

not attested not anchored not stored refs pending

The Modular Symmetry of Markov Maps

Jan Cameron, Jon Bannon, Kunal Mukherjee

arxiv:1905.06729 v1 · 2019-05-16 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HA6UAW375RY7RX5UKKIAK44UHK}

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	2026-05-17T23:46:01.219719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

383d405b7fec71f8dfb452900573943ab679cea9380321be4016370cb34665e0

Aliases

arxiv: 1905.06729 · arxiv_version: 1905.06729v1 · doi: 10.48550/arxiv.1905.06729 · pith_short_12: HA6UAW375RY7 · pith_short_16: HA6UAW375RY7RX5U · pith_short_8: HA6UAW37

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/HA6UAW375RY7RX5UKKIAK44UHK \
  | 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: 383d405b7fec71f8dfb452900573943ab679cea9380321be4016370cb34665e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac5e0ecb69c3777aacc5b9a77b108df2789263c4ac4462a9d9ad6dbb93a27e52",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-05-16T13:23:10Z",
    "title_canon_sha256": "9c52974526045b9cab8f159d37f1e50a73478cf1391780ea7f9615fbf723a8de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.06729",
    "kind": "arxiv",
    "version": 1
  }
}