Pith Number

pith:AEH2PAE6

pith:2015:AEH2PAE6NFIEWXPIX4GW4KWCGR

not attested not anchored not stored refs pending

Slope inequality for families of curves over surfaces

Tong Zhang

arxiv:1512.03933 v2 · 2015-12-12 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AEH2PAE6NFIEWXPIX4GW4KWCGR}

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	2026-05-18T01:12:55.106939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

010fa7809e69504b5de8bf0d6e2ac2344d6f4b0576c3a19deed9c34388d953ff

Aliases

arxiv: 1512.03933 · arxiv_version: 1512.03933v2 · doi: 10.48550/arxiv.1512.03933 · pith_short_12: AEH2PAE6NFIE · pith_short_16: AEH2PAE6NFIEWXPI · pith_short_8: AEH2PAE6

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/AEH2PAE6NFIEWXPIX4GW4KWCGR \
  | 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: 010fa7809e69504b5de8bf0d6e2ac2344d6f4b0576c3a19deed9c34388d953ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6dc7064a8dbb096266fd66d62dc4dc46b3950b6012fb16939494742d71f6443",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-12-12T16:43:17Z",
    "title_canon_sha256": "e1041156724af7a0e0c383cb34e5a329f1d2603856392e4b173a59aa498eb3d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03933",
    "kind": "arxiv",
    "version": 2
  }
}