{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FFO72H3VQIZ7N2VNISNNBLS2RF","short_pith_number":"pith:FFO72H3V","canonical_record":{"source":{"id":"1404.5705","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-23T05:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"c92519432d15d612cc00c88d0ad05f60db76bbfc053d37363bb5a7be54a5eaca","abstract_canon_sha256":"ea6755f52ab522113cbfd68eb22687790c347076a1ee79ac18d95f13359e0015"},"schema_version":"1.0"},"canonical_sha256":"295dfd1f758233f6eaad449ad0ae5a8952231381c3bf7a8798feb5672ea766c3","source":{"kind":"arxiv","id":"1404.5705","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5705","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5705v7","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5705","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"FFO72H3VQIZ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FFO72H3VQIZ7N2VN","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FFO72H3V","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FFO72H3VQIZ7N2VNISNNBLS2RF","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5705","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-23T05:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"c92519432d15d612cc00c88d0ad05f60db76bbfc053d37363bb5a7be54a5eaca","abstract_canon_sha256":"ea6755f52ab522113cbfd68eb22687790c347076a1ee79ac18d95f13359e0015"},"schema_version":"1.0"},"canonical_sha256":"295dfd1f758233f6eaad449ad0ae5a8952231381c3bf7a8798feb5672ea766c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:03.619796Z","signature_b64":"oq1Y12e2XbjGWc8aX6cfnZ8E8jUu1L9Uh3Q5xZtaDr59TOO7eWBD6ky+JU9bBvMQPBoeDCSh8eR4bZtUk+VxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"295dfd1f758233f6eaad449ad0ae5a8952231381c3bf7a8798feb5672ea766c3","last_reissued_at":"2026-05-17T23:57:03.619035Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:03.619035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5705","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sbc9TbJAN+yRFBHDm/4COyL9ifrKCHbgg9ftVXX8qL8NQDBb+CU3/ysg3ihnksBzRF3kTt0lmiD5q7jtcPc3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:00:05.458861Z"},"content_sha256":"71e0b5f829fa2d90c93c93b1aba07d5da93c61dc97ced8db01d85384e2b7ca01","schema_version":"1.0","event_id":"sha256:71e0b5f829fa2d90c93c93b1aba07d5da93c61dc97ced8db01d85384e2b7ca01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FFO72H3VQIZ7N2VNISNNBLS2RF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Component sizes for large quantum erdos renyi graph near criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir Dembo, Anna Levit, Sreekar Vadlamani","submitted_at":"2014-04-23T05:21:54Z","abstract_excerpt":"The $N$ vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson process. Considering these graphs at their critical parameters, we show that the joint law of the re-scaled by $N^{2/3}$ and ordered sizes of their connected components, converges to that of the ordered lengths of excursions above zero for a reflected Brownian motion with drift. Thereby, this work forms the first example of an inhomogeneous random graph, beyond th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5705","kind":"arxiv","version":7},"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":"2026-05-17T23:57:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAOYhvoM/TuKgac70b3x8JvrJ6/geZGsvqxuV217BA+BzTPk/dy5+WzVWzOkHVdVUvv01ejEkcZKCHrivEySBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:00:05.459199Z"},"content_sha256":"a258a2d9a5cf5f6cc70611ae87eafc57872600557e7b12229d2e0214f44e1e15","schema_version":"1.0","event_id":"sha256:a258a2d9a5cf5f6cc70611ae87eafc57872600557e7b12229d2e0214f44e1e15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFO72H3VQIZ7N2VNISNNBLS2RF/bundle.json","state_url":"https://pith.science/pith/FFO72H3VQIZ7N2VNISNNBLS2RF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFO72H3VQIZ7N2VNISNNBLS2RF/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":"2026-06-23T12:00:05Z","links":{"resolver":"https://pith.science/pith/FFO72H3VQIZ7N2VNISNNBLS2RF","bundle":"https://pith.science/pith/FFO72H3VQIZ7N2VNISNNBLS2RF/bundle.json","state":"https://pith.science/pith/FFO72H3VQIZ7N2VNISNNBLS2RF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFO72H3VQIZ7N2VNISNNBLS2RF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FFO72H3VQIZ7N2VNISNNBLS2RF","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":"ea6755f52ab522113cbfd68eb22687790c347076a1ee79ac18d95f13359e0015","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-23T05:21:54Z","title_canon_sha256":"c92519432d15d612cc00c88d0ad05f60db76bbfc053d37363bb5a7be54a5eaca"},"schema_version":"1.0","source":{"id":"1404.5705","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5705","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5705v7","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5705","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"FFO72H3VQIZ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FFO72H3VQIZ7N2VN","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FFO72H3V","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:a258a2d9a5cf5f6cc70611ae87eafc57872600557e7b12229d2e0214f44e1e15","target":"graph","created_at":"2026-05-17T23:57:03Z","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 $N$ vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson process. Considering these graphs at their critical parameters, we show that the joint law of the re-scaled by $N^{2/3}$ and ordered sizes of their connected components, converges to that of the ordered lengths of excursions above zero for a reflected Brownian motion with drift. Thereby, this work forms the first example of an inhomogeneous random graph, beyond th","authors_text":"Amir Dembo, Anna Levit, Sreekar Vadlamani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-23T05:21:54Z","title":"Component sizes for large quantum erdos renyi graph near criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5705","kind":"arxiv","version":7},"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":"sha256:71e0b5f829fa2d90c93c93b1aba07d5da93c61dc97ced8db01d85384e2b7ca01","target":"record","created_at":"2026-05-17T23:57:03Z","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":"ea6755f52ab522113cbfd68eb22687790c347076a1ee79ac18d95f13359e0015","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-23T05:21:54Z","title_canon_sha256":"c92519432d15d612cc00c88d0ad05f60db76bbfc053d37363bb5a7be54a5eaca"},"schema_version":"1.0","source":{"id":"1404.5705","kind":"arxiv","version":7}},"canonical_sha256":"295dfd1f758233f6eaad449ad0ae5a8952231381c3bf7a8798feb5672ea766c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"295dfd1f758233f6eaad449ad0ae5a8952231381c3bf7a8798feb5672ea766c3","first_computed_at":"2026-05-17T23:57:03.619035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:03.619035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oq1Y12e2XbjGWc8aX6cfnZ8E8jUu1L9Uh3Q5xZtaDr59TOO7eWBD6ky+JU9bBvMQPBoeDCSh8eR4bZtUk+VxCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:03.619796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5705","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71e0b5f829fa2d90c93c93b1aba07d5da93c61dc97ced8db01d85384e2b7ca01","sha256:a258a2d9a5cf5f6cc70611ae87eafc57872600557e7b12229d2e0214f44e1e15"],"state_sha256":"1af938e4117539b9c8b931710c4ff04f211d27f6e0bb2b2a831eee0ce9f35eb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hv/lGOi7PpzfX5DJRaPaWP4x5KeIB9r/nwhjR0Js/t/SqLkJBsuQzfMF+YEeHsfe8g4PtzmJzStMO7dCswvJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:00:05.461149Z","bundle_sha256":"047043590901bf7f57adf7aed20c93569e3785e7adfe6862002a3554abcbfbe3"}}