Pith Number

pith:4FCW3LWF

pith:2016:4FCW3LWFQ7UBPUEXQP7PUYZ656

not attested not anchored not stored refs pending

A Homology Theory For A Special Family Of Semi-groups

Sujoy Mukherjee

arxiv:1611.05555 v1 · 2016-11-17 · math.GT · 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{4FCW3LWFQ7UBPUEXQP7PUYZ656}

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	2026-05-18T00:58:03.278372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1456daec587e817d09783fefa633eefa421c205299db9f4298dce2ea5469cee

Aliases

arxiv: 1611.05555 · arxiv_version: 1611.05555v1 · doi: 10.48550/arxiv.1611.05555 · pith_short_12: 4FCW3LWFQ7UB · pith_short_16: 4FCW3LWFQ7UBPUEX · pith_short_8: 4FCW3LWF

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/4FCW3LWFQ7UBPUEXQP7PUYZ656 \
  | 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: e1456daec587e817d09783fefa633eefa421c205299db9f4298dce2ea5469cee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "815ba1beb07e34b5d30313529b3cece1707813eddd24a14916cace9e384e4332",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-17T03:53:39Z",
    "title_canon_sha256": "5fbf94346210b967bd45f814e0953b850379627ea98e2c967e1b4b579992fd43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05555",
    "kind": "arxiv",
    "version": 1
  }
}