Pith Number

pith:TRFZRT3Y

pith:2013:TRFZRT3YQORC2RQ6VIKR2Y2NCR

not attested not anchored not stored refs pending

4-manifolds, surgery on loops and geometric realization of Tietze transformations

Wojciech Politarczyk

arxiv:1303.6502 v3 · 2013-03-26 · math.GT · 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{TRFZRT3YQORC2RQ6VIKR2Y2NCR}

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	2026-05-18T03:29:26.411398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c4b98cf7883a22d461eaa151d634d14430891d9a1c7070232f27feccd90244c

Aliases

arxiv: 1303.6502 · arxiv_version: 1303.6502v3 · doi: 10.48550/arxiv.1303.6502 · pith_short_12: TRFZRT3YQORC · pith_short_16: TRFZRT3YQORC2RQ6 · pith_short_8: TRFZRT3Y

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/TRFZRT3YQORC2RQ6VIKR2Y2NCR \
  | 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: 9c4b98cf7883a22d461eaa151d634d14430891d9a1c7070232f27feccd90244c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "479b06dc6a0f8fe5be65e30caeff2e5fca63cdae7690919c732b6de5ed6a99b3",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-03-26T14:14:42Z",
    "title_canon_sha256": "8429b620efba8933d0082c2f5706dbb9b5184edacdf6f335434c61d2f3b362c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6502",
    "kind": "arxiv",
    "version": 3
  }
}