Pith Number

pith:5K3VOY5H

pith:2025:5K3VOY5HGMOC2EBDTZEV33IU6X

not attested not anchored not stored refs pending

Tropical Ptolemy Transformations and Invariants of Braids

Gurnoor Singh

arxiv:2506.12085 v1 · 2025-06-10 · 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{5K3VOY5HGMOC2EBDTZEV33IU6X}

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	2026-07-05T11:21:16.803777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eab75763a7331c2d10239e495ded14f5ca18dc0723b96f05745a620b9a01abb8

Aliases

arxiv: 2506.12085 · arxiv_version: 2506.12085v1 · doi: 10.48550/arxiv.2506.12085 · pith_short_12: 5K3VOY5HGMOC · pith_short_16: 5K3VOY5HGMOC2EBD · pith_short_8: 5K3VOY5H

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/5K3VOY5HGMOC2EBDTZEV33IU6X \
  | 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: eab75763a7331c2d10239e495ded14f5ca18dc0723b96f05745a620b9a01abb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "415149a07601d30df5a4e69494d0b5c545bb2f11cb9265c49d2a83c756a3d5cf",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-06-10T09:59:19Z",
    "title_canon_sha256": "57d7b89f872274ae1ec4f8d8a185f4646ff3f97019030ce1948a2334bbada24b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.12085",
    "kind": "arxiv",
    "version": 1
  }
}