Pith Number

pith:PHFQSOWI

pith:2016:PHFQSOWITQNHJA6NUHRQU3HN72

not attested not anchored not stored refs pending

Binary Operations for Homotopy Groups with Coefficients

Martin Arkowitz

arxiv:1605.08708 v2 · 2016-05-27 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHFQSOWITQNHJA6NUHRQU3HN72}

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	2026-05-18T00:36:43.830660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79cb093ac89c1a7483cda1e30a6cedfe8e917799f8de822270fa93109a93efed

Aliases

arxiv: 1605.08708 · arxiv_version: 1605.08708v2 · doi: 10.48550/arxiv.1605.08708 · pith_short_12: PHFQSOWITQNH · pith_short_16: PHFQSOWITQNHJA6N · pith_short_8: PHFQSOWI

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/PHFQSOWITQNHJA6NUHRQU3HN72 \
  | 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: 79cb093ac89c1a7483cda1e30a6cedfe8e917799f8de822270fa93109a93efed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21ddf5a08aca53ad1cb15e973c6fb243a89323c5bdb4dd142bd72f7f0f8da764",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-05-27T16:22:33Z",
    "title_canon_sha256": "6ee55b113de99d6d334b0bbf69798169639283ba193fd21a99c703ed3937864e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.08708",
    "kind": "arxiv",
    "version": 2
  }
}