Pith Number

pith:7DVACDSW

pith:2015:7DVACDSWPDKK5J7VGKIPLGVTTX

not attested not anchored not stored refs pending

The equivalence of the torus and the product of two circles in homotopy type theory

Kristina Sojakova

arxiv:1510.03918 v1 · 2015-10-13 · 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{7DVACDSWPDKK5J7VGKIPLGVTTX}

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	2026-05-18T01:30:09.806024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8ea010e5678d4aea7f53290f59ab39de9584e8dc793dab650940b78e7a2cab2

Aliases

arxiv: 1510.03918 · arxiv_version: 1510.03918v1 · doi: 10.48550/arxiv.1510.03918 · pith_short_12: 7DVACDSWPDKK · pith_short_16: 7DVACDSWPDKK5J7V · pith_short_8: 7DVACDSW

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/7DVACDSWPDKK5J7VGKIPLGVTTX \
  | 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: f8ea010e5678d4aea7f53290f59ab39de9584e8dc793dab650940b78e7a2cab2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd29cb577ffad0b51840443b6378c2ed0819ce0f81268eb0e72a666b473038f8",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2015-10-13T22:38:45Z",
    "title_canon_sha256": "e7428a15dcd28f56f8fb10f4bd42a2069a2a7c39dbc04e23fdaabae079d23209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03918",
    "kind": "arxiv",
    "version": 1
  }
}