Pith Number

pith:FZLOFVT4

pith:2016:FZLOFVT4JDEIXNOS5FW26P5I4F

not attested not anchored not stored refs pending

Nielsen equivalence in mapping tori over the torus

Ian Biringer

arxiv:1610.07528 v2 · 2016-10-24 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FZLOFVT4JDEIXNOS5FW26P5I4F}

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	2026-05-18T00:39:47.289299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e56e2d67c48c88bb5d2e96daf3fa8e144c1285f1c2a49675b0f8573c967ece7

Aliases

arxiv: 1610.07528 · arxiv_version: 1610.07528v2 · doi: 10.48550/arxiv.1610.07528 · pith_short_12: FZLOFVT4JDEI · pith_short_16: FZLOFVT4JDEIXNOS · pith_short_8: FZLOFVT4

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/FZLOFVT4JDEIXNOS5FW26P5I4F \
  | 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: 2e56e2d67c48c88bb5d2e96daf3fa8e144c1285f1c2a49675b0f8573c967ece7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04432139df9c68927e6e8d4b946f8e9fca8119ed7910cbc3487c50d0734e5b29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-10-24T18:29:44Z",
    "title_canon_sha256": "5031de7ad552195db730950d0c69244b4f77ab0fc179b7ab980ff1bfce97ff68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07528",
    "kind": "arxiv",
    "version": 2
  }
}