Pith Number

pith:CXJRZTBG

pith:2015:CXJRZTBGAF2DQPVJDO5FICNV33

not attested not anchored not stored refs pending

Optimal injective stability for the symplectic $K_1Sp$ group

Anjan Gupta

arxiv:1511.09419 v1 · 2015-11-30 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CXJRZTBGAF2DQPVJDO5FICNV33}

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	2026-05-18T01:25:40.293857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15d31ccc260174383ea91bba5409b5dee6f0bc80e41927b039f59a1026d3ee88

Aliases

arxiv: 1511.09419 · arxiv_version: 1511.09419v1 · doi: 10.48550/arxiv.1511.09419 · pith_short_12: CXJRZTBGAF2D · pith_short_16: CXJRZTBGAF2DQPVJ · pith_short_8: CXJRZTBG

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/CXJRZTBGAF2DQPVJDO5FICNV33 \
  | 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: 15d31ccc260174383ea91bba5409b5dee6f0bc80e41927b039f59a1026d3ee88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccacdc8d763ddd4d302853eb997384f1e7593e7ef4773fb7decfab380d11c2db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-11-30T18:31:21Z",
    "title_canon_sha256": "c712e071825a9aed2f8a5e34d2af82ce1089f61a82e5cdb6fe3278c0c92a1ed9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09419",
    "kind": "arxiv",
    "version": 1
  }
}