Pith Number

pith:TSMXNW76

pith:2016:TSMXNW76QIQCJRNJLLTZSIGW4K

not attested not anchored not stored refs pending

On the homotopy groups of spheres in homotopy type theory

Guillaume Brunerie

arxiv:1606.05916 v1 · 2016-06-19 · math.AT · cs.LO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TSMXNW76QIQCJRNJLLTZSIGW4K}

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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

Classifying Types

Delooping presented groups in homotopy type theory

Receipt and verification

First computed	2026-05-18T01:12:15.821372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c9976dbfe822024c5a95ae79920d6e29599f5bff4e3cc54b5efe5ba783050f7

Aliases

arxiv: 1606.05916 · arxiv_version: 1606.05916v1 · doi: 10.48550/arxiv.1606.05916 · pith_short_12: TSMXNW76QIQC · pith_short_16: TSMXNW76QIQCJRNJ · pith_short_8: TSMXNW76

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/TSMXNW76QIQCJRNJLLTZSIGW4K \
  | 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: 9c9976dbfe822024c5a95ae79920d6e29599f5bff4e3cc54b5efe5ba783050f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bcd749491caf1c52c0bcf4f9efcf2a7e8725ab1fb6413edbd66ee871965dd7e",
    "cross_cats_sorted": [
      "cs.LO",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-06-19T22:10:45Z",
    "title_canon_sha256": "26f61206d29a95e97c569c6399c33351ab1ebe340bb3f71ea4b3b658431ae37a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05916",
    "kind": "arxiv",
    "version": 1
  }
}