Pith Number

pith:TFMAFKOH

pith:2018:TFMAFKOHENK7SVWXE4N2YU2MPZ

not attested not anchored not stored refs pending

Comodules, contramodules and Pontryagin duality

John MacQuarrie, Ricardo Souza

arxiv:1806.03714 v1 · 2018-06-10 · math.RT · math.CT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TFMAFKOHENK7SVWXE4N2YU2MPZ}

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	2026-05-18T00:13:24.861839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

995802a9c72355f956d7271bac534c7e43f2a1660f5c49fa8bed97dc5bb3bdb4

Aliases

arxiv: 1806.03714 · arxiv_version: 1806.03714v1 · doi: 10.48550/arxiv.1806.03714 · pith_short_12: TFMAFKOHENK7 · pith_short_16: TFMAFKOHENK7SVWX · pith_short_8: TFMAFKOH

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/TFMAFKOHENK7SVWXE4N2YU2MPZ \
  | 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: 995802a9c72355f956d7271bac534c7e43f2a1660f5c49fa8bed97dc5bb3bdb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfe56f41213b3d4366867f9eb48ea118a6da2ce0037f630881f98ba6525f9706",
    "cross_cats_sorted": [
      "math.CT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2018-06-10T19:51:57Z",
    "title_canon_sha256": "613064b6e75fac1874b76761b69a368162ba124dcb228294105a2c01456b4b38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.03714",
    "kind": "arxiv",
    "version": 1
  }
}