{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AEMQ2IVYOS42G4D64VQPTXDZIA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c697a63b3a6601f4580e40b92794d1508f6529ce29af9bf2f26fc288de1f32d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-07-11T16:23:16Z","title_canon_sha256":"3c15e6ec2bd2b8e84d03d45d999a58112ca78877232a6a7fa665d91c02564b39"},"schema_version":"1.0","source":{"id":"1507.03124","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03124","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03124v2","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03124","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"AEMQ2IVYOS42","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AEMQ2IVYOS42G4D6","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AEMQ2IVY","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:c15b015ba2bf8380046451a8fff552a4c2019c1cb10628529b054ff15ce062e7","target":"graph","created_at":"2026-05-18T01:29:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We analyze a set of volume limited samples from SDSS DR12 to quantify the degree of inhomogeneity at different length scales using Shannon entropy. We find that the galaxy distributions exhibit a higher degree of inhomogeneity as compared to a Poisson point process at all length scales. Our analysis indicates that signatures of inhomogeneities in the galaxy distributions persist at least upto a length scale of $120 \\, h^{-1}\\, {\\rm Mpc}$. The galaxy distributions appear to be homogeneous on a scale of $140 \\, h^{-1}\\, {\\rm Mpc}$ and beyond. Analyzing a set of mock galaxy samples from a semi an","authors_text":"Biswajit Pandey, Suman Sarkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-07-11T16:23:16Z","title":"Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03124","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:555247f6b5ab3394134768ad664d8feed34660e30832b182c7a62cf337c78d36","target":"record","created_at":"2026-05-18T01:29:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c697a63b3a6601f4580e40b92794d1508f6529ce29af9bf2f26fc288de1f32d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-07-11T16:23:16Z","title_canon_sha256":"3c15e6ec2bd2b8e84d03d45d999a58112ca78877232a6a7fa665d91c02564b39"},"schema_version":"1.0","source":{"id":"1507.03124","kind":"arxiv","version":2}},"canonical_sha256":"01190d22b874b9a3707ee560f9dc794038d7756f1a7eff1b63fbebe0e588d0d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01190d22b874b9a3707ee560f9dc794038d7756f1a7eff1b63fbebe0e588d0d3","first_computed_at":"2026-05-18T01:29:45.424227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:45.424227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYnkRIYDhjxa1WrM08t7XJD0nEh6AQ38XvVe8wZnJtySh1i73G0S8bXxMI7I6W5XaeNxGw4hRRC6ZIdYznWeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:45.424715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03124","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:555247f6b5ab3394134768ad664d8feed34660e30832b182c7a62cf337c78d36","sha256:c15b015ba2bf8380046451a8fff552a4c2019c1cb10628529b054ff15ce062e7"],"state_sha256":"084fa42b3f6c0b427980a260013a2316eae05d6a62c59eb4fe5e4b50bfcc59b6"}