Pith Number

pith:UL7MJL6I

pith:2021:UL7MJL6ITHSKPWH7MWW7CR7UDS

not attested not anchored not stored refs pending

Kaleidoscopic Symmetries and Self-Similarity of Integral Apollonian Gaskets

Indubala I Satija

arxiv:2104.13198 v1 · 2021-04-21 · math.GM · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UL7MJL6ITHSKPWH7MWW7CR7UDS}

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.

Cited by

1 paper in Pith

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory

Receipt and verification

First computed	2026-07-05T02:35:46.334027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2fec4afc899e4a7d8ff65adf147f41cbaa5b7a3f870cd0604f1395fd7c54fce

Aliases

arxiv: 2104.13198 · arxiv_version: 2104.13198v1 · doi: 10.48550/arxiv.2104.13198 · pith_short_12: UL7MJL6ITHSK · pith_short_16: UL7MJL6ITHSKPWH7 · pith_short_8: UL7MJL6I

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/UL7MJL6ITHSKPWH7MWW7CR7UDS \
  | 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: a2fec4afc899e4a7d8ff65adf147f41cbaa5b7a3f870cd0604f1395fd7c54fce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0827030c1c36e51f1477541da8295ff3a62634005a44fb515c59216cea43961",
    "cross_cats_sorted": [
      "nlin.SI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2021-04-21T14:11:54Z",
    "title_canon_sha256": "a840fe3fdea84de4caa801b4306bf1b32f42a9c8b0107bc2feec80ff9885b14e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.13198",
    "kind": "arxiv",
    "version": 1
  }
}