Pith Number

pith:ZW4UUH45

pith:2025:ZW4UUH45ODR2UPQQ37O2QBQU5S

not attested not anchored not stored refs pending

3-manifolds with more than one abelian embedding

Jonathan A. Hillman

arxiv:2506.01186 v2 · 2025-06-01 · 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{ZW4UUH45ODR2UPQQ37O2QBQU5S}

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	2026-07-05T11:15:21.843463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdb94a1f9d70e3aa3e10dfdda80614ec86927cbe1a30adddfc3c216918951bbf

Aliases

arxiv: 2506.01186 · arxiv_version: 2506.01186v2 · doi: 10.48550/arxiv.2506.01186 · pith_short_12: ZW4UUH45ODR2 · pith_short_16: ZW4UUH45ODR2UPQQ · pith_short_8: ZW4UUH45

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/ZW4UUH45ODR2UPQQ37O2QBQU5S \
  | 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: cdb94a1f9d70e3aa3e10dfdda80614ec86927cbe1a30adddfc3c216918951bbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "723ecaff90645b77ef3590c945606f9b6987489d66bf6855c8190183d1d5cb45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-06-01T21:46:17Z",
    "title_canon_sha256": "d70a06fdf070700ff39ae4f4af29c9c9d0f3acff5213e858c1d59a61231c12c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.01186",
    "kind": "arxiv",
    "version": 2
  }
}