Pith Number

pith:FFHZFXL4

pith:2014:FFHZFXL4PTCQACGHI4HYE3AIWX

not attested not anchored not stored refs pending

Engel relations in 4-manifold topology

Michael Freedman, Vyacheslav Krushkal

arxiv:1412.5024 v3 · 2014-12-16 · math.GT · math.GR

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

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	2026-05-18T00:09:42.584161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

294f92dd7c7cc50008c7470f826c08b5dc1f3e42636289358f6b59039bed8ff4

Aliases

arxiv: 1412.5024 · arxiv_version: 1412.5024v3 · doi: 10.48550/arxiv.1412.5024 · pith_short_12: FFHZFXL4PTCQ · pith_short_16: FFHZFXL4PTCQACGH · pith_short_8: FFHZFXL4

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/FFHZFXL4PTCQACGHI4HYE3AIWX \
  | 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: 294f92dd7c7cc50008c7470f826c08b5dc1f3e42636289358f6b59039bed8ff4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8555cc4b44a07cae05ccf3808856938b2649a523dae073841a8871c76ac1033",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-12-16T14:53:17Z",
    "title_canon_sha256": "e47983fc0e8c99db952d12b2415460b93b19bcb1d8df4cc7ad90dd4270692fae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.5024",
    "kind": "arxiv",
    "version": 3
  }
}