Pith Number

pith:TSKZIMMF

pith:2015:TSKZIMMFLMXW2NE6U2BPBCJBYR

not attested not anchored not stored refs pending

The mapping $i_{2}$ on the free paratopological groups

Chuan Liu, Fucai Lin

arxiv:1507.05646 v1 · 2015-07-20 · math.GR · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TSKZIMMFLMXW2NE6U2BPBCJBYR}

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	2026-05-18T01:36:32.843347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c959431855b2f6d349ea682f08921c45818edb6b522f03538a81181be6c599b

Aliases

arxiv: 1507.05646 · arxiv_version: 1507.05646v1 · doi: 10.48550/arxiv.1507.05646 · pith_short_12: TSKZIMMFLMXW · pith_short_16: TSKZIMMFLMXW2NE6 · pith_short_8: TSKZIMMF

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/TSKZIMMFLMXW2NE6U2BPBCJBYR \
  | 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: 9c959431855b2f6d349ea682f08921c45818edb6b522f03538a81181be6c599b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bc65d5b76e73f17f703f91e52ecdc5baf93901d18a1056893b3ed4477f3715b",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-20T20:39:32Z",
    "title_canon_sha256": "8ded00ec2850e579ee36b91c617f12204d17e2b6b666576b6f6d8d898578e911"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05646",
    "kind": "arxiv",
    "version": 1
  }
}