Pith Number

pith:T334Y6EM

pith:2009:T334Y6EM6VEBNT3PYJXPCE3265

not attested not anchored not stored refs pending

Mod-two cohomology of symmetric groups as a Hopf ring

Chad Giusti, Dev Sinha, Paolo Salvatore

arxiv:0909.3292 v3 · 2009-09-17 · math.AT · math.KT · 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{T334Y6EM6VEBNT3PYJXPCE3265}

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	2026-05-18T02:58:02.761449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ef7cc788cf54816cf6fc26ef1137af774b44a29299292c8e08891e503564cea

Aliases

arxiv: 0909.3292 · arxiv_version: 0909.3292v3 · doi: 10.48550/arxiv.0909.3292 · pith_short_12: T334Y6EM6VEB · pith_short_16: T334Y6EM6VEBNT3P · pith_short_8: T334Y6EM

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/T334Y6EM6VEBNT3PYJXPCE3265 \
  | 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: 9ef7cc788cf54816cf6fc26ef1137af774b44a29299292c8e08891e503564cea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cb565aefd94ecac9f10a34245de82ecfa0dd8983186bb418eb605022a1c9a56",
    "cross_cats_sorted": [
      "math.KT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-09-17T18:35:27Z",
    "title_canon_sha256": "fe55d65db93060c3287ae27ac950b23fad949a0cbb7615227aa8b58a110a4fad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3292",
    "kind": "arxiv",
    "version": 3
  }
}