Pith Number

pith:X3RHLI6M

pith:2021:X3RHLI6M3FGBGAOATE55FVHNQ2

not attested not anchored not stored refs pending

Maps from 3-manifolds to 4-manifolds that induce isomorphisms on $\pi_1$

Hongbin Sun, Zhongzi Wang

arxiv:2108.05784 v3 · 2021-08-12 · 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{X3RHLI6M3FGBGAOATE55FVHNQ2}

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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.

Cited by

1 paper in Pith

$\pi_1$-injective bounding and application to 3- and 4-manifolds

Receipt and verification

First computed	2026-07-05T06:05:55.226401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bee275a3ccd94c1301c0993bd2d4ed86aeaa2e51750d1b6662fb0817b29d9878

Aliases

arxiv: 2108.05784 · arxiv_version: 2108.05784v3 · doi: 10.48550/arxiv.2108.05784 · pith_short_12: X3RHLI6M3FGB · pith_short_16: X3RHLI6M3FGBGAOA · pith_short_8: X3RHLI6M

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/X3RHLI6M3FGBGAOATE55FVHNQ2 \
  | 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: bee275a3ccd94c1301c0993bd2d4ed86aeaa2e51750d1b6662fb0817b29d9878

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a59605eee45b2288ad9d9301cd68cf1469796a61255a989832d91d6b05476ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-08-12T14:53:20Z",
    "title_canon_sha256": "8da0ba51491b03f502abeeb6d9265248f88dea7e3288e40b95067a2c9bf6de00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.05784",
    "kind": "arxiv",
    "version": 3
  }
}