Pith Number

pith:TQ7LZSZ3

pith:1993:TQ7LZSZ3H72O6FQDFSRV7OLU4S

not attested not anchored not stored refs pending

Mirror Symmetry of K3 and Torus

Katsuyuki Sugiyama, Masaru Nagura

arxiv:hep-th/9312159 v1 · 1993-12-20 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQ7LZSZ3H72O6FQDFSRV7OLU4S}

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	2026-05-18T01:38:42.169774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c3ebccb3b3ff4ef16032ca35fb974e485cde7e819f29a67b2b14e74a37d2a02

Aliases

arxiv: hep-th/9312159 · arxiv_version: hep-th/9312159v1 · doi: 10.48550/arxiv.hep-th/9312159 · pith_short_12: TQ7LZSZ3H72O · pith_short_16: TQ7LZSZ3H72O6FQD · pith_short_8: TQ7LZSZ3

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/TQ7LZSZ3H72O6FQDFSRV7OLU4S \
  | 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: 9c3ebccb3b3ff4ef16032ca35fb974e485cde7e819f29a67b2b14e74a37d2a02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e44c2a8a1dd703b8708db2c7c788d4f8e0ceb894b590b8feac90fd041c5d7045",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1993-12-20T10:51:07Z",
    "title_canon_sha256": "36163ba475ae620ec8e8f41f1653105279ca89304afcadd329088adb39b43186"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9312159",
    "kind": "arxiv",
    "version": 1
  }
}