Pith Number

pith:3XGDCZCL

pith:2015:3XGDCZCLAQXYI6PFFUJUUVNOVV

not attested not anchored not stored refs pending

Almost-invariant and essentially-invariant halfspaces

Ben Wallis, Gleb Sirotkin

arxiv:1509.07428 v2 · 2015-09-24 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XGDCZCLAQXYI6PFFUJUUVNOVV}

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	2026-05-18T01:31:10.403550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddcc31644b042f8479e52d134a55aead751d1bc6278b8aea38007826877d4a49

Aliases

arxiv: 1509.07428 · arxiv_version: 1509.07428v2 · doi: 10.48550/arxiv.1509.07428 · pith_short_12: 3XGDCZCLAQXY · pith_short_16: 3XGDCZCLAQXYI6PF · pith_short_8: 3XGDCZCL

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/3XGDCZCLAQXYI6PFFUJUUVNOVV \
  | 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: ddcc31644b042f8479e52d134a55aead751d1bc6278b8aea38007826877d4a49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfee5d4aecdde8228c9d0064c2fa7149350af15905a44760cc41387f58c0652a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-09-24T16:43:06Z",
    "title_canon_sha256": "a284b781dc26425779df70ac92afc7fd671b0e75dd6612d8988c69ce6dc78564"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07428",
    "kind": "arxiv",
    "version": 2
  }
}