Pith Number

pith:FNTE3S4H

pith:2012:FNTE3S4H2EAJVE3HAOGWUGS2YR

not attested not anchored not stored refs pending

Notes on the Sigma invariants

Ralph Strebel

arxiv:1204.0214 v2 · 2012-04-01 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNTE3S4H2EAJVE3HAOGWUGS2YR}

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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

2 papers in Pith

Actions with a strong fundamental domain and Sigma invariants of groups

On the BNSR invariants of link groups

Receipt and verification

First computed	2026-05-18T03:32:08.011086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b664dcb87d1009a9367038d6a1a5ac46149a8cc83e77a11f2b8dae06bf386cf

Aliases

arxiv: 1204.0214 · arxiv_version: 1204.0214v2 · doi: 10.48550/arxiv.1204.0214 · pith_short_12: FNTE3S4H2EAJ · pith_short_16: FNTE3S4H2EAJVE3H · pith_short_8: FNTE3S4H

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/FNTE3S4H2EAJVE3HAOGWUGS2YR \
  | 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: 2b664dcb87d1009a9367038d6a1a5ac46149a8cc83e77a11f2b8dae06bf386cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "210376c9e52922da3628c3b10e389b0cde2c6110badce34c3adc3dc7fc87ade0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-01T14:09:33Z",
    "title_canon_sha256": "06219be89c937d5fa686db50195b1e208a6f2eec3d348d8f89c9c3b8672c6686"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0214",
    "kind": "arxiv",
    "version": 2
  }
}