{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BJXLMEHHQ6VINPZADXTJ6WIADQ","short_pith_number":"pith:BJXLMEHH","canonical_record":{"source":{"id":"1710.08043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-23T00:03:51Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"5a7e01533eb063a56e6e055a25298bcc73eee5a548620a5919d5300f9a80720e","abstract_canon_sha256":"5ae8b5d77e4a56b820c7778f1faf344696872e8992170b37bf6f36012dbb3563"},"schema_version":"1.0"},"canonical_sha256":"0a6eb610e787aa86bf201de69f59001c38f50469e074bc5eba1836c9ae76d480","source":{"kind":"arxiv","id":"1710.08043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08043","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08043v1","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08043","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"BJXLMEHHQ6VI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BJXLMEHHQ6VINPZA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BJXLMEHH","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BJXLMEHHQ6VINPZADXTJ6WIADQ","target":"record","payload":{"canonical_record":{"source":{"id":"1710.08043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-23T00:03:51Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"5a7e01533eb063a56e6e055a25298bcc73eee5a548620a5919d5300f9a80720e","abstract_canon_sha256":"5ae8b5d77e4a56b820c7778f1faf344696872e8992170b37bf6f36012dbb3563"},"schema_version":"1.0"},"canonical_sha256":"0a6eb610e787aa86bf201de69f59001c38f50469e074bc5eba1836c9ae76d480","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:11.226680Z","signature_b64":"tRT8+iotn8ZwvKbE71aK3owgauAqR7NtIwoakq3AUzEjKomRs0AWQM8w57zCx4eIwl2R1nJ7gisr/xs5tqprBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a6eb610e787aa86bf201de69f59001c38f50469e074bc5eba1836c9ae76d480","last_reissued_at":"2026-05-18T00:10:11.225963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:11.225963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.08043","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":"2026-05-18T00:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ioJeWCOrO8Mjo6hgsLmlRDMQ1jK4GlEMET4SgH47/r/2YWm22OfwXyqGDWL09ZY/uT2ZCTUo7B6B8A6qhBUbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:22:40.825010Z"},"content_sha256":"be167beff0f1c7335308044c93883a8338cf9cdef68235fa8b8ccaa4d66dacfb","schema_version":"1.0","event_id":"sha256:be167beff0f1c7335308044c93883a8338cf9cdef68235fa8b8ccaa4d66dacfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BJXLMEHHQ6VINPZADXTJ6WIADQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Product-Sum universality and Rushbrooke inequality in explosive percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"M. K. Hassan, M. M. H. Sabbir","submitted_at":"2017-10-23T00:03:51Z","abstract_excerpt":"We study explosive percolation (EP) on Erd\\\"{o}s-R\\'{e}nyi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition, now it is well-accepted as a probabilistic model for thermal continuous phase transition (CPT). However, no model for CPT is complete unless we know how to relate its observable quantities with those of thermal CPT. To this end, we define entropy, specific heat, re-define susceptibility and show that they behave exactly like their thermal counterparts. We obtain the critical exponents $\\nu, \\alpha, \\beta$ and $\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08043","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":"2026-05-18T00:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IrlY+hPDDAyFth4LSw+G2/oXRFtoROe16vmvw5IzU8Dz47U7/lOCnxBjBQwlkY9FI/RG7LLFfFVujzkZc6b+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:22:40.825796Z"},"content_sha256":"bc6cec56fac132f78ded816302fae31ba2a2b331d70c626954c74541bb8640e1","schema_version":"1.0","event_id":"sha256:bc6cec56fac132f78ded816302fae31ba2a2b331d70c626954c74541bb8640e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ/bundle.json","state_url":"https://pith.science/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ/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":"2026-05-30T09:22:40Z","links":{"resolver":"https://pith.science/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ","bundle":"https://pith.science/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ/bundle.json","state":"https://pith.science/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJXLMEHHQ6VINPZADXTJ6WIADQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BJXLMEHHQ6VINPZADXTJ6WIADQ","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":"5ae8b5d77e4a56b820c7778f1faf344696872e8992170b37bf6f36012dbb3563","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-23T00:03:51Z","title_canon_sha256":"5a7e01533eb063a56e6e055a25298bcc73eee5a548620a5919d5300f9a80720e"},"schema_version":"1.0","source":{"id":"1710.08043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08043","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08043v1","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08043","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"BJXLMEHHQ6VI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BJXLMEHHQ6VINPZA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BJXLMEHH","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:bc6cec56fac132f78ded816302fae31ba2a2b331d70c626954c74541bb8640e1","target":"graph","created_at":"2026-05-18T00:10:11Z","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 study explosive percolation (EP) on Erd\\\"{o}s-R\\'{e}nyi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition, now it is well-accepted as a probabilistic model for thermal continuous phase transition (CPT). However, no model for CPT is complete unless we know how to relate its observable quantities with those of thermal CPT. To this end, we define entropy, specific heat, re-define susceptibility and show that they behave exactly like their thermal counterparts. We obtain the critical exponents $\\nu, \\alpha, \\beta$ and $\\g","authors_text":"M. K. Hassan, M. M. H. Sabbir","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-23T00:03:51Z","title":"Product-Sum universality and Rushbrooke inequality in explosive percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08043","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:be167beff0f1c7335308044c93883a8338cf9cdef68235fa8b8ccaa4d66dacfb","target":"record","created_at":"2026-05-18T00:10:11Z","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":"5ae8b5d77e4a56b820c7778f1faf344696872e8992170b37bf6f36012dbb3563","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-23T00:03:51Z","title_canon_sha256":"5a7e01533eb063a56e6e055a25298bcc73eee5a548620a5919d5300f9a80720e"},"schema_version":"1.0","source":{"id":"1710.08043","kind":"arxiv","version":1}},"canonical_sha256":"0a6eb610e787aa86bf201de69f59001c38f50469e074bc5eba1836c9ae76d480","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6eb610e787aa86bf201de69f59001c38f50469e074bc5eba1836c9ae76d480","first_computed_at":"2026-05-18T00:10:11.225963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:11.225963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tRT8+iotn8ZwvKbE71aK3owgauAqR7NtIwoakq3AUzEjKomRs0AWQM8w57zCx4eIwl2R1nJ7gisr/xs5tqprBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:11.226680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be167beff0f1c7335308044c93883a8338cf9cdef68235fa8b8ccaa4d66dacfb","sha256:bc6cec56fac132f78ded816302fae31ba2a2b331d70c626954c74541bb8640e1"],"state_sha256":"c59318d623c15228c723b2fd106baecf8b53d7820e25ba0204e1e6848ff4772c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0nyuZMxyMqWhWMRmp/HlcjmHHGADRHDc1qpGRZnLIpqsrcfl9AUGqSZAXNrfw+zzl1gk5ed8c2beLl3OKOD0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:22:40.828438Z","bundle_sha256":"26cbb30c4896a597a92ff663bb4feacf1be0286d34a1d7697da523bf2e89eb9b"}}