{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MRCHVY57HH43DSNSGSMCENMQWK","short_pith_number":"pith:MRCHVY57","canonical_record":{"source":{"id":"1703.06001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-17T13:19:23Z","cross_cats_sorted":[],"title_canon_sha256":"6298f0f77e0e61938987312e28092976fcae19067bcee1fe39abdcec99706698","abstract_canon_sha256":"6e3df91640b39941704c8e48dd42af96d139a23892e316fcaa47ee8418d11901"},"schema_version":"1.0"},"canonical_sha256":"64447ae3bf39f9b1c9b23498223590b2b00d539da75f6cfcf00c5811cc4796a6","source":{"kind":"arxiv","id":"1703.06001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06001","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06001v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06001","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"MRCHVY57HH43","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MRCHVY57HH43DSNS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MRCHVY57","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MRCHVY57HH43DSNSGSMCENMQWK","target":"record","payload":{"canonical_record":{"source":{"id":"1703.06001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-17T13:19:23Z","cross_cats_sorted":[],"title_canon_sha256":"6298f0f77e0e61938987312e28092976fcae19067bcee1fe39abdcec99706698","abstract_canon_sha256":"6e3df91640b39941704c8e48dd42af96d139a23892e316fcaa47ee8418d11901"},"schema_version":"1.0"},"canonical_sha256":"64447ae3bf39f9b1c9b23498223590b2b00d539da75f6cfcf00c5811cc4796a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:29.744216Z","signature_b64":"0UP0gnM5pcCA2yNb1W0sVcImu8Q2t/as/P9gYyD+PfWlr6znIakLJnduubEVcfd4+G9d30Iq0XGeOiDt1TIOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64447ae3bf39f9b1c9b23498223590b2b00d539da75f6cfcf00c5811cc4796a6","last_reissued_at":"2026-05-18T00:48:29.743567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:29.743567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.06001","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1cjsLhMatnHe2eOs4x8D+ENX3V/gOiHLrr0eZkX0bkM3ry6n9nhR+Pcmcee7cy33T66/dB+DKJVLoNcSCJAzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:51:19.216365Z"},"content_sha256":"32ec53e2cbfcd15703531e0b99d4dfb880abb93c00903844530b3590d5b959dd","schema_version":"1.0","event_id":"sha256:32ec53e2cbfcd15703531e0b99d4dfb880abb93c00903844530b3590d5b959dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MRCHVY57HH43DSNSGSMCENMQWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The use of spatial information in entropy measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Daniela Cocchi, Giulia Roli, Linda Altieri","submitted_at":"2017-03-17T13:19:23Z","abstract_excerpt":"The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at accounting for space in entropy measures, as a generalization when the spatial location of occurrences ought to be accounted for. The main limit of these developments is that all indices are computed conditional on a chosen distance. This work follows and extends the route for including spatial components in entropy measures. Starting from the probabilistic proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06001","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9SCMFneiQnRWLyMbb0PjVT7jSip3IK/dfXQ/1avhAtb1h5qnRJxqa5LRLXuS3Frpl5Oa33SjyNC4j9Q4lWIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:51:19.216834Z"},"content_sha256":"fb65d2faf9b3e5e6097d91cd48963fcae91662f49c2249aafe12a8ea3712f74f","schema_version":"1.0","event_id":"sha256:fb65d2faf9b3e5e6097d91cd48963fcae91662f49c2249aafe12a8ea3712f74f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRCHVY57HH43DSNSGSMCENMQWK/bundle.json","state_url":"https://pith.science/pith/MRCHVY57HH43DSNSGSMCENMQWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRCHVY57HH43DSNSGSMCENMQWK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T04:51:19Z","links":{"resolver":"https://pith.science/pith/MRCHVY57HH43DSNSGSMCENMQWK","bundle":"https://pith.science/pith/MRCHVY57HH43DSNSGSMCENMQWK/bundle.json","state":"https://pith.science/pith/MRCHVY57HH43DSNSGSMCENMQWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRCHVY57HH43DSNSGSMCENMQWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MRCHVY57HH43DSNSGSMCENMQWK","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":"6e3df91640b39941704c8e48dd42af96d139a23892e316fcaa47ee8418d11901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-17T13:19:23Z","title_canon_sha256":"6298f0f77e0e61938987312e28092976fcae19067bcee1fe39abdcec99706698"},"schema_version":"1.0","source":{"id":"1703.06001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06001","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06001v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06001","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"MRCHVY57HH43","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MRCHVY57HH43DSNS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MRCHVY57","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:fb65d2faf9b3e5e6097d91cd48963fcae91662f49c2249aafe12a8ea3712f74f","target":"graph","created_at":"2026-05-18T00:48:29Z","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":"The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at accounting for space in entropy measures, as a generalization when the spatial location of occurrences ought to be accounted for. The main limit of these developments is that all indices are computed conditional on a chosen distance. This work follows and extends the route for including spatial components in entropy measures. Starting from the probabilistic proper","authors_text":"Daniela Cocchi, Giulia Roli, Linda Altieri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-17T13:19:23Z","title":"The use of spatial information in entropy measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06001","kind":"arxiv","version":1},"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":"sha256:32ec53e2cbfcd15703531e0b99d4dfb880abb93c00903844530b3590d5b959dd","target":"record","created_at":"2026-05-18T00:48:29Z","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":"6e3df91640b39941704c8e48dd42af96d139a23892e316fcaa47ee8418d11901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-17T13:19:23Z","title_canon_sha256":"6298f0f77e0e61938987312e28092976fcae19067bcee1fe39abdcec99706698"},"schema_version":"1.0","source":{"id":"1703.06001","kind":"arxiv","version":1}},"canonical_sha256":"64447ae3bf39f9b1c9b23498223590b2b00d539da75f6cfcf00c5811cc4796a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64447ae3bf39f9b1c9b23498223590b2b00d539da75f6cfcf00c5811cc4796a6","first_computed_at":"2026-05-18T00:48:29.743567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:29.743567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0UP0gnM5pcCA2yNb1W0sVcImu8Q2t/as/P9gYyD+PfWlr6znIakLJnduubEVcfd4+G9d30Iq0XGeOiDt1TIOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:29.744216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32ec53e2cbfcd15703531e0b99d4dfb880abb93c00903844530b3590d5b959dd","sha256:fb65d2faf9b3e5e6097d91cd48963fcae91662f49c2249aafe12a8ea3712f74f"],"state_sha256":"bc61d21d66349329cf2432b168bdae79447d66abecde4f33739d7416a0437286"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rFYNmRGRZMD1BXu2ZKc01JDqqTzn4nrc97d7gIv3Ru+0a/rwXfJ6Erz5LsxQjEzCGEVwrVbVa5m8CT8LVCigAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:51:19.221480Z","bundle_sha256":"d473bb040e5c5d88050ef8c62055270ce6f9fbeb76e66677ca4c9ab0212be986"}}