Pith Number

pith:R5N5ZDVO

pith:2014:R5N5ZDVOCKG5FITTCFXW7DHM6Q

not attested not anchored not stored refs pending

Relative second bounded cohomology of free groups

Cristina Pagliantini, Pascal Rolli

arxiv:1407.4053 v2 · 2014-07-15 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R5N5ZDVOCKG5FITTCFXW7DHM6Q}

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	2026-05-18T02:20:10.313368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f5bdc8eae128dd2a273116f6f8cecf42cc826d42ffb42302fc6010f9931b5cb

Aliases

arxiv: 1407.4053 · arxiv_version: 1407.4053v2 · doi: 10.48550/arxiv.1407.4053 · pith_short_12: R5N5ZDVOCKG5 · pith_short_16: R5N5ZDVOCKG5FITT · pith_short_8: R5N5ZDVO

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/R5N5ZDVOCKG5FITTCFXW7DHM6Q \
  | 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: 8f5bdc8eae128dd2a273116f6f8cecf42cc826d42ffb42302fc6010f9931b5cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13373a6f27a6b669b810f094edb45d4ef5d8ce7c4922289727db776e5b48ba5a",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-07-15T16:49:46Z",
    "title_canon_sha256": "34923d610940a3b96cf6ff263f264f33721561ddd4e813ca58b9cbd0ce00ae63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.4053",
    "kind": "arxiv",
    "version": 2
  }
}