Pith Number

pith:YSDL2UHJ

pith:2018:YSDL2UHJRSCTFBYVGKDAOEDIFB

not attested not anchored not stored refs pending

SYZ mirror symmetry from Witten-Morse theory

Ziming Nikolas Ma

arxiv:1811.09042 v1 · 2018-11-22 · math.DG · math.AG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YSDL2UHJRSCTFBYVGKDAOEDIFB}

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	2026-05-18T00:00:07.223932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c486bd50e98c853287153286071068287dbd8030c1d3ff455c77c8d8b2a6f9bd

Aliases

arxiv: 1811.09042 · arxiv_version: 1811.09042v1 · doi: 10.48550/arxiv.1811.09042 · pith_short_12: YSDL2UHJRSCT · pith_short_16: YSDL2UHJRSCTFBYV · pith_short_8: YSDL2UHJ

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/YSDL2UHJRSCTFBYVGKDAOEDIFB \
  | 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: c486bd50e98c853287153286071068287dbd8030c1d3ff455c77c8d8b2a6f9bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b5c9fc5df63356fb32b10ff16d21145119b97f33dabb885f54b3aae5aab6297",
    "cross_cats_sorted": [
      "math.AG",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-11-22T07:16:38Z",
    "title_canon_sha256": "dc9c23fc4cf8a7ec79f3ff56b404c08681a52bca630b7661e6c338f340fc39db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.09042",
    "kind": "arxiv",
    "version": 1
  }
}