{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HV7OPT2J4OPI2GPBO52HQBVA5P","short_pith_number":"pith:HV7OPT2J","canonical_record":{"source":{"id":"1402.5819","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-24T13:28:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9dae415b3ba5de50820bd5ebf0a61b8de2d39ed300b3c97742eec427969621ea","abstract_canon_sha256":"56655359226b8e69090b1a525b5b5b71cbe47cd8676537d5bcc5c3c2a5096870"},"schema_version":"1.0"},"canonical_sha256":"3d7ee7cf49e39e8d19e177747806a0ebc26c7e6ac5ff48aeed77c229bb4a8e37","source":{"kind":"arxiv","id":"1402.5819","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5819","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5819v3","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5819","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"HV7OPT2J4OPI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HV7OPT2J4OPI2GPB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HV7OPT2J","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HV7OPT2J4OPI2GPBO52HQBVA5P","target":"record","payload":{"canonical_record":{"source":{"id":"1402.5819","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-24T13:28:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9dae415b3ba5de50820bd5ebf0a61b8de2d39ed300b3c97742eec427969621ea","abstract_canon_sha256":"56655359226b8e69090b1a525b5b5b71cbe47cd8676537d5bcc5c3c2a5096870"},"schema_version":"1.0"},"canonical_sha256":"3d7ee7cf49e39e8d19e177747806a0ebc26c7e6ac5ff48aeed77c229bb4a8e37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:29.053303Z","signature_b64":"sqZCEddd2ga3A3XNfRByOmNUkZ6oKUNVQDjKjJzjgDRy5JH/bydfaGg11SOom+6JnqfblsU4pQbw0ZUsJOMnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d7ee7cf49e39e8d19e177747806a0ebc26c7e6ac5ff48aeed77c229bb4a8e37","last_reissued_at":"2026-05-18T01:44:29.052777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:29.052777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.5819","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TMBWJskma1bPCXExowFRWJdt4UZLJm4epxvkiEIu6FuiWg2vtOSaeTtPSvPqmJy4cGwf8m5MMUQkOBb/qfK4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:42:56.569829Z"},"content_sha256":"6a1da06f379303e1f7bb6478fb9fd4a1a4b33501cf6ae935be98a9edf825712e","schema_version":"1.0","event_id":"sha256:6a1da06f379303e1f7bb6478fb9fd4a1a4b33501cf6ae935be98a9edf825712e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HV7OPT2J4OPI2GPBO52HQBVA5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walk on random infinite looptrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Jakob E. Bj\\\"ornberg, Sigurdur \\\"Orn Stef\\'ansson","submitted_at":"2014-02-24T13:28:24Z","abstract_excerpt":"Looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation. Here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical Galton--Watson tree conditioned to be large. We study simple random walk on these infinite looptrees by means of providing estimates on volume and resistance growth. We prove that if the offspring distribution of the Galton--Watson process is in the domain of attraction of a stable distribution with index $\\alpha\\in(1,2]$ then the spectral dimension of the looptree is $2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5819","kind":"arxiv","version":3},"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":"2026-05-18T01:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zru4hJGUmOK+vMwpdkdcQKneMA16Yl65VO+fqeCFqA9bKwSrjjtXQj228BY9cfZBofznKHgMO/WTaozH+y2gAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:42:56.570573Z"},"content_sha256":"18d1758d8ed0e2ccdb6906a68eee58113c719e2e62a5364f8f10fc7215adc872","schema_version":"1.0","event_id":"sha256:18d1758d8ed0e2ccdb6906a68eee58113c719e2e62a5364f8f10fc7215adc872"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HV7OPT2J4OPI2GPBO52HQBVA5P/bundle.json","state_url":"https://pith.science/pith/HV7OPT2J4OPI2GPBO52HQBVA5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HV7OPT2J4OPI2GPBO52HQBVA5P/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":"2026-05-27T04:42:56Z","links":{"resolver":"https://pith.science/pith/HV7OPT2J4OPI2GPBO52HQBVA5P","bundle":"https://pith.science/pith/HV7OPT2J4OPI2GPBO52HQBVA5P/bundle.json","state":"https://pith.science/pith/HV7OPT2J4OPI2GPBO52HQBVA5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HV7OPT2J4OPI2GPBO52HQBVA5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HV7OPT2J4OPI2GPBO52HQBVA5P","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":"56655359226b8e69090b1a525b5b5b71cbe47cd8676537d5bcc5c3c2a5096870","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-24T13:28:24Z","title_canon_sha256":"9dae415b3ba5de50820bd5ebf0a61b8de2d39ed300b3c97742eec427969621ea"},"schema_version":"1.0","source":{"id":"1402.5819","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5819","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5819v3","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5819","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"HV7OPT2J4OPI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HV7OPT2J4OPI2GPB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HV7OPT2J","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:18d1758d8ed0e2ccdb6906a68eee58113c719e2e62a5364f8f10fc7215adc872","target":"graph","created_at":"2026-05-18T01:44:29Z","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":"Looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation. Here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical Galton--Watson tree conditioned to be large. We study simple random walk on these infinite looptrees by means of providing estimates on volume and resistance growth. We prove that if the offspring distribution of the Galton--Watson process is in the domain of attraction of a stable distribution with index $\\alpha\\in(1,2]$ then the spectral dimension of the looptree is $2","authors_text":"Jakob E. Bj\\\"ornberg, Sigurdur \\\"Orn Stef\\'ansson","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-24T13:28:24Z","title":"Random walk on random infinite looptrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5819","kind":"arxiv","version":3},"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":"sha256:6a1da06f379303e1f7bb6478fb9fd4a1a4b33501cf6ae935be98a9edf825712e","target":"record","created_at":"2026-05-18T01:44:29Z","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":"56655359226b8e69090b1a525b5b5b71cbe47cd8676537d5bcc5c3c2a5096870","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-24T13:28:24Z","title_canon_sha256":"9dae415b3ba5de50820bd5ebf0a61b8de2d39ed300b3c97742eec427969621ea"},"schema_version":"1.0","source":{"id":"1402.5819","kind":"arxiv","version":3}},"canonical_sha256":"3d7ee7cf49e39e8d19e177747806a0ebc26c7e6ac5ff48aeed77c229bb4a8e37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d7ee7cf49e39e8d19e177747806a0ebc26c7e6ac5ff48aeed77c229bb4a8e37","first_computed_at":"2026-05-18T01:44:29.052777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:29.052777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqZCEddd2ga3A3XNfRByOmNUkZ6oKUNVQDjKjJzjgDRy5JH/bydfaGg11SOom+6JnqfblsU4pQbw0ZUsJOMnAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:29.053303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5819","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a1da06f379303e1f7bb6478fb9fd4a1a4b33501cf6ae935be98a9edf825712e","sha256:18d1758d8ed0e2ccdb6906a68eee58113c719e2e62a5364f8f10fc7215adc872"],"state_sha256":"ed9c97a93d3d8d22b3cd1694200fcd98ea505d03085b5bcd7d227a00a8086b51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWL/F6IGz5q/heFwRfj4Vk0vbBKRNxiSpZpqihouS7g7U6HJ8NC17MRq7pCi9oz7H2TO6ZDNBFepFEZ3WXQaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:42:56.573879Z","bundle_sha256":"9181f4591fad57aebb251e6484f3fe94528a3dc64910d558b14d835c18f5753d"}}