{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TE3EV7E2DQFCLPEFWTEJFWSSFW","short_pith_number":"pith:TE3EV7E2","canonical_record":{"source":{"id":"1902.05774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-15T11:38:30Z","cross_cats_sorted":[],"title_canon_sha256":"acd0cd085143a36efed7089af5edfc0678953847e690b23eb1e9351d4ec5f147","abstract_canon_sha256":"5c96e6ea08f6f188adb047776efeecef49ccb67cc09a11adc9cd1937bd3eb1a6"},"schema_version":"1.0"},"canonical_sha256":"99364afc9a1c0a25bc85b4c892da522da63d4776f1bc89f28a764232fae05044","source":{"kind":"arxiv","id":"1902.05774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05774","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05774v1","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05774","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"pith_short_12","alias_value":"TE3EV7E2DQFC","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TE3EV7E2DQFCLPEF","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TE3EV7E2","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TE3EV7E2DQFCLPEFWTEJFWSSFW","target":"record","payload":{"canonical_record":{"source":{"id":"1902.05774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-15T11:38:30Z","cross_cats_sorted":[],"title_canon_sha256":"acd0cd085143a36efed7089af5edfc0678953847e690b23eb1e9351d4ec5f147","abstract_canon_sha256":"5c96e6ea08f6f188adb047776efeecef49ccb67cc09a11adc9cd1937bd3eb1a6"},"schema_version":"1.0"},"canonical_sha256":"99364afc9a1c0a25bc85b4c892da522da63d4776f1bc89f28a764232fae05044","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:56.181648Z","signature_b64":"I3SX2ZkuLJbN7qXRL3aiO7Nrwd0cymJrr0VZDUr5CVwIUZeKSF/Rjy8bCp2i65KaE1cn4DU07eJeK0ELq2ZaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99364afc9a1c0a25bc85b4c892da522da63d4776f1bc89f28a764232fae05044","last_reissued_at":"2026-05-17T23:53:56.180944Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:56.180944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.05774","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":"2026-05-17T23:53:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYCIUdaBGI5aX/AqR9vK9Ljes++N5BWGfn8pNUg+Ovca1Jq4DlPZJOnIA2vFtgcsrrpz1/JUhjmD0TBFFrVrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:12:12.959626Z"},"content_sha256":"8adcda733a3ceebd38d526c71b3508719db6ca4e60479270473cb3a0ea466c9e","schema_version":"1.0","event_id":"sha256:8adcda733a3ceebd38d526c71b3508719db6ca4e60479270473cb3a0ea466c9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TE3EV7E2DQFCLPEFWTEJFWSSFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scale-free percolation in continuum space: quenched degree and clustering coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joseba Dalmau, Michele Salvi","submitted_at":"2019-02-15T11:38:30Z","abstract_excerpt":"Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\\mathbb R^d$. Each vertex is equipped with a random weight and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05774","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":"2026-05-17T23:53:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EXb1tZ2qNFF5IU1i2o/ifvthkGrdxJlHX9Nk1hO2UUOrB72U4H3TBVtrcsVoamw43HFxWxnQeEjVuNYErkwbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:12:12.960327Z"},"content_sha256":"2f4e1bba216cf5da213f5fec815592fdae8ce18cc6c6de436300642487b306ff","schema_version":"1.0","event_id":"sha256:2f4e1bba216cf5da213f5fec815592fdae8ce18cc6c6de436300642487b306ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW/bundle.json","state_url":"https://pith.science/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW/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":"2026-06-11T21:12:12Z","links":{"resolver":"https://pith.science/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW","bundle":"https://pith.science/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW/bundle.json","state":"https://pith.science/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TE3EV7E2DQFCLPEFWTEJFWSSFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TE3EV7E2DQFCLPEFWTEJFWSSFW","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":"5c96e6ea08f6f188adb047776efeecef49ccb67cc09a11adc9cd1937bd3eb1a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-15T11:38:30Z","title_canon_sha256":"acd0cd085143a36efed7089af5edfc0678953847e690b23eb1e9351d4ec5f147"},"schema_version":"1.0","source":{"id":"1902.05774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05774","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05774v1","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05774","created_at":"2026-05-17T23:53:56Z"},{"alias_kind":"pith_short_12","alias_value":"TE3EV7E2DQFC","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TE3EV7E2DQFCLPEF","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TE3EV7E2","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:2f4e1bba216cf5da213f5fec815592fdae8ce18cc6c6de436300642487b306ff","target":"graph","created_at":"2026-05-17T23:53:56Z","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":"Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\\mathbb R^d$. Each vertex is equipped with a random weight and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree dis","authors_text":"Joseba Dalmau, Michele Salvi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-15T11:38:30Z","title":"Scale-free percolation in continuum space: quenched degree and clustering coefficient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05774","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":"sha256:8adcda733a3ceebd38d526c71b3508719db6ca4e60479270473cb3a0ea466c9e","target":"record","created_at":"2026-05-17T23:53:56Z","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":"5c96e6ea08f6f188adb047776efeecef49ccb67cc09a11adc9cd1937bd3eb1a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-15T11:38:30Z","title_canon_sha256":"acd0cd085143a36efed7089af5edfc0678953847e690b23eb1e9351d4ec5f147"},"schema_version":"1.0","source":{"id":"1902.05774","kind":"arxiv","version":1}},"canonical_sha256":"99364afc9a1c0a25bc85b4c892da522da63d4776f1bc89f28a764232fae05044","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99364afc9a1c0a25bc85b4c892da522da63d4776f1bc89f28a764232fae05044","first_computed_at":"2026-05-17T23:53:56.180944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:56.180944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3SX2ZkuLJbN7qXRL3aiO7Nrwd0cymJrr0VZDUr5CVwIUZeKSF/Rjy8bCp2i65KaE1cn4DU07eJeK0ELq2ZaAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:56.181648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8adcda733a3ceebd38d526c71b3508719db6ca4e60479270473cb3a0ea466c9e","sha256:2f4e1bba216cf5da213f5fec815592fdae8ce18cc6c6de436300642487b306ff"],"state_sha256":"f2780e0c2f191cb866eff3d10d7a7cc2de06a68749781908f510272396385fca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ib2bcRu6aMwIh9AGg+Kki8w/xxYVw6UTJ70lORovHrz4Q5NTWegOwqFp+nRqZ84Z7JILqLnrzz32IGE1OSF4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:12:12.967033Z","bundle_sha256":"bc1251730c8ba8e81fc295339306ca54017f0d2f473a3615096f3674e89772ec"}}