Pith Number

pith:E7TRPQN2

pith:2015:E7TRPQN2JKW3HM63TGLEXRHA2L

not attested not anchored not stored refs pending

Amenable groups and smooth topology of 4-manifolds

Emmy Murphy, Larry Guth, Michael Freedman

arxiv:1503.05497 v1 · 2015-03-18 · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E7TRPQN2JKW3HM63TGLEXRHA2L}

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	2026-05-18T02:21:26.263139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27e717c1ba4aadb3b3db99964bc4e0d2f87755896421a4b919e5dc733a81e04d

Aliases

arxiv: 1503.05497 · arxiv_version: 1503.05497v1 · doi: 10.48550/arxiv.1503.05497 · pith_short_12: E7TRPQN2JKW3 · pith_short_16: E7TRPQN2JKW3HM63 · pith_short_8: E7TRPQN2

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/E7TRPQN2JKW3HM63TGLEXRHA2L \
  | 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: 27e717c1ba4aadb3b3db99964bc4e0d2f87755896421a4b919e5dc733a81e04d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a9cbc0185b2a175ae6fe13b239ba81e90f48613ae2184bbecf07357f1baad6b",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-03-18T17:23:25Z",
    "title_canon_sha256": "69cabaaa50b2c5e01a717c1c7125c6fd1e4295164a833a1dcd547b1289fc62fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.05497",
    "kind": "arxiv",
    "version": 1
  }
}