Pith Number

pith:3FGQFHIQ

pith:2026:3FGQFHIQVYYHRSCZZCTWO2CHZU

not attested not anchored not stored refs pending

Exotic knottings and symmetries of surfaces in 4-manifolds

Nathan Sunukjian, R. Inanc Baykur

arxiv:2607.27751 v1 · 2026-07-30 · math.GT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3FGQFHIQVYYHRSCZZCTWO2CHZU}

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	2026-07-31T01:30:28.480245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

d94d029d10ae3078c859c8a7676847cd048c9c2da0613bf24ee94181d8028b7a

Aliases

arxiv: 2607.27751 · arxiv_version: 2607.27751v1 · doi: 10.48550/arxiv.2607.27751 · pith_short_12: 3FGQFHIQVYYH · pith_short_16: 3FGQFHIQVYYHRSCZ · pith_short_8: 3FGQFHIQ

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/3FGQFHIQVYYHRSCZZCTWO2CHZU \
  | 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: d94d029d10ae3078c859c8a7676847cd048c9c2da0613bf24ee94181d8028b7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4bf049281f1391190f7af9c7da7da406cdd9f4f7984b4d90a5b8b120190f94f",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-30T06:46:28Z",
    "title_canon_sha256": "4c4e707b610d1a1d6e95a4445ad9f999b2a52f7c5647d631aefd297c98e82e71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27751",
    "kind": "arxiv",
    "version": 1
  }
}