Pith Number

pith:AMYJARSS

pith:2012:AMYJARSS6XS5NJJTMYNQEH7WYQ

not attested not anchored not stored refs pending

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

Takao Satoh

arxiv:1204.0876 v2 · 2012-04-04 · math.AT · math.GR

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\usepackage{pith}
\pithnumber{AMYJARSS6XS5NJJTMYNQEH7WYQ}

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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.

Cited by

1 paper in Pith

Johnson homomorphisms and the second rational cohomology of handlebody Torelli groups

Receipt and verification

First computed	2026-05-18T03:21:31.878841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0330904652f5e5d6a533661b021ff6c43ca8742aaeba5d911cec4f95871fa306

Aliases

arxiv: 1204.0876 · arxiv_version: 1204.0876v2 · doi: 10.48550/arxiv.1204.0876 · pith_short_12: AMYJARSS6XS5 · pith_short_16: AMYJARSS6XS5NJJT · pith_short_8: AMYJARSS

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/AMYJARSS6XS5NJJTMYNQEH7WYQ \
  | 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: 0330904652f5e5d6a533661b021ff6c43ca8742aaeba5d911cec4f95871fa306

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cf8e16fdda375445a76e4fbafd7b544265ebcc047f88bdef01a6e7b2c08447b",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-04-04T06:48:45Z",
    "title_canon_sha256": "d59b0fb239ae08711358771aab4409613cce5a35744706443989d7431785eae0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0876",
    "kind": "arxiv",
    "version": 2
  }
}