Pith Number

pith:W7342WN5

pith:2018:W7342WN57LMAYP447MMNBJFMJE

not attested not anchored not stored refs pending

Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$

Tadayuki Watanabe

arxiv:1812.02448 v3 · 2018-12-06 · math.GT · math.AT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W7342WN57LMAYP447MMNBJFMJE}

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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

4 papers in Pith

Infinite-dimensionality of the rational homotopy groups of the space of long embeddings of codimension 2

The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds

Diffeomorphism groups and gauge theory for families

Gauge theory for families

Receipt and verification

First computed	2026-07-04T23:58:05.369370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7f7cd59bdfad80c3f9cfb18d0a4ac490fe622398e6fe504a219ce1cb5bfaa5b

Aliases

arxiv: 1812.02448 · arxiv_version: 1812.02448v3 · doi: 10.48550/arxiv.1812.02448 · pith_short_12: W7342WN57LMA · pith_short_16: W7342WN57LMAYP44 · pith_short_8: W7342WN5

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/W7342WN57LMAYP447MMNBJFMJE \
  | 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: b7f7cd59bdfad80c3f9cfb18d0a4ac490fe622398e6fe504a219ce1cb5bfaa5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e7dd68ac403f53f0cfc8c637bee67c02b0b1a708e8e67dd2aa80641e3484f91",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-12-06T10:36:42Z",
    "title_canon_sha256": "31ef5f15f1a8edf54f48d14f708f6109fac55e53c4af104a4f53ecd419dce78a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.02448",
    "kind": "arxiv",
    "version": 3
  }
}