Pith Number

pith:PFUE2RG3

pith:2011:PFUE2RG3LBBDVKE6A76BKSQOR7

not attested not anchored not stored refs pending

The rational cohomology of the mapping class group vanishes in its virtual cohomological dimension

Andrew Putman, Benson Farb, Thomas Church

arxiv:1108.0622 v3 · 2011-08-02 · math.GT · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PFUE2RG3LBBDVKE6A76BKSQOR7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T03:00:27.204723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79684d44db58423aa89e07fc154a0e8fddbc989478396d38891163a7bef40863

Aliases

arxiv: 1108.0622 · arxiv_version: 1108.0622v3 · doi: 10.48550/arxiv.1108.0622 · pith_short_12: PFUE2RG3LBBD · pith_short_16: PFUE2RG3LBBDVKE6 · pith_short_8: PFUE2RG3

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/PFUE2RG3LBBDVKE6A76BKSQOR7 \
  | 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: 79684d44db58423aa89e07fc154a0e8fddbc989478396d38891163a7bef40863

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebb6f77dfbc42c0c8327b777f07b4688716122f8e4fa03dc68fb489a6cd041e4",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-02T17:15:39Z",
    "title_canon_sha256": "b253f4a18430da61a010ded02ad5afd42ccb1a2fda2082cee8932ba0664cb1d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0622",
    "kind": "arxiv",
    "version": 3
  }
}